For what value of k do the equations 2x 3y 2 0 and 4x 6y k 0 represent coincident lines?

Question

ParallelConsistentIntersectingPerpendicular to each other

There are countless possible answers for a system of linear equations. The number that makes every equation in a system of linear equations true is the system's solution. The answers to the two variables in the two equations will be these points' coordinates.In this question we have asked that given set of equations 3x +2y = 8 and 2x – 3y = 1 are Consistent, Inconsistent, Intersecting, or Perpendicular to each other.

The correct answer is: Consistent

We have given the equations as: 3x +2y = 8 and 2x – 3y = 1.Comparing both the equations with a1, b1, c1 and a2, b2, c2, we get:a1=3, b1=2, c1=8a2=2, b2=-3, c2=1Now equating then, we get:Therefore the system is consistent. 

Here in this question, we were given two equations 3x +2y = 8 and 2x – 3y = 1, where we were supposed to find the system is consistent or not so using the system of linear equations, we found that the system is consistent.

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Related Questions to study

Mathematics

The lines 2x + 5y=17 and 5x + 3y=14 are ______________.

A system of linear equations is said to be inconsistent if it has at least one solution.
The given equations are :
2x + 5y = 17
5x + 3y = 14
Comparing both the equations with a1, b1, c1 and a2, b2, c2, we get:
a1 = 2, b1 = 5, c1 = -17 and a2 = 5, b2 = 3, c2 = -14
Now equating it, we get:
 
Clearly, 
Hence, it will have a unique solution.
The given equations are consistent.

The lines 2x + 5y=17 and 5x + 3y=14 are ______________.

MathematicsGrade-8

A system of linear equations is said to be inconsistent if it has at least one solution.
The given equations are :
2x + 5y = 17
5x + 3y = 14
Comparing both the equations with a1, b1, c1 and a2, b2, c2, we get:
a1 = 2, b1 = 5, c1 = -17 and a2 = 5, b2 = 3, c2 = -14
Now equating it, we get:
 
Clearly, 
Hence, it will have a unique solution.
The given equations are consistent.

Mathematics

The lines 5x - 7y = 13 and 10x - 14y = 15 are ___________.

A system of linear equations is said to be inconsistent if it has no solution at all.
Now we have given thee equations as:
5x - 7y = 13
10x - 14y = 15
Comparing both the equations with a1, b1, c1 and a2, b2, c2, we get:
a1 = 5, b1 = - 7, c1 = -13
a2 = 10, b2 = - 14, c2 = -15
Lets equate it, we get:
 
Clearly,

Hence, it will have no solution
The given equations are inconsistent.

The lines 5x - 7y = 13 and 10x - 14y = 15 are ___________.

MathematicsGrade-8

A system of linear equations is said to be inconsistent if it has no solution at all.
Now we have given thee equations as:
5x - 7y = 13
10x - 14y = 15
Comparing both the equations with a1, b1, c1 and a2, b2, c2, we get:
a1 = 5, b1 = - 7, c1 = -13
a2 = 10, b2 = - 14, c2 = -15
Lets equate it, we get:
 
Clearly,

Hence, it will have no solution
The given equations are inconsistent.

Mathematics

What will be the value of k, if the lines given by x + ky + 3 and 2x + (k + 2)y + 6 are coincident?

We have given that the lines are coincident lines. A system of linear equations has infinite solutions when the graphs are the exact same line.

Lines are coincident, so

Now

Simplifying it, we get:

So the value of k is 2.

What will be the value of k, if the lines given by x + ky + 3 and 2x + (k + 2)y + 6 are coincident?

MathematicsGrade-8

We have given that the lines are coincident lines. A system of linear equations has infinite solutions when the graphs are the exact same line.

Lines are coincident, so

Now

Simplifying it, we get:

So the value of k is 2.

Mathematics

What will be the value of k, if the lines given by 3x + ky - 4 and 5x + (9 + k)y + 41 represent two lines intersecting at a point?

The intersecting lines (two or more) never cross over at more than one location.
Any angle can be used to intersect the lines in any direction. Always greater than 0° and less than 180°, this angle is generated.

Lines are intersecting at a point, so

Now: 

Cross multiplying it, we get:

So k is not equal to 27/2.

What will be the value of k, if the lines given by 3x + ky - 4 and 5x + (9 + k)y + 41 represent two lines intersecting at a point?

MathematicsGrade-8

The intersecting lines (two or more) never cross over at more than one location.
Any angle can be used to intersect the lines in any direction. Always greater than 0° and less than 180°, this angle is generated.

Lines are intersecting at a point, so

Now: 

Cross multiplying it, we get:

So k is not equal to 27/2.

Mathematics

What will be the value of k, if the lines given by (5 + k)x - 3y + 15 and (k - 1)x - y + 19 are parallel?

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

Lines are parallel, so 
Now,

So the value of k is 4.

What will be the value of k, if the lines given by (5 + k)x - 3y + 15 and (k - 1)x - y + 19 are parallel?

MathematicsGrade-8

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

Lines are parallel, so 
Now,

So the value of k is 4.

Mathematics

What will be the nature of the graph lines of the equations 2x + 5y + 15 and 6x + 15y + 45?

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

The given equations are 2x + 5y + 15 and 6x + 15y + 45.
Here,  and 
Now, 
Clearly, 
Therefore, the graph lines of the equations will be coincident.

What will be the nature of the graph lines of the equations 2x + 5y + 15 and 6x + 15y + 45?

MathematicsGrade-8

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

The given equations are 2x + 5y + 15 and 6x + 15y + 45.
Here,  and 
Now, 
Clearly, 
Therefore, the graph lines of the equations will be coincident.

Mathematics

What will be the nature of the graph lines of the equations x + 3y - 2 and 2x - y + 5?

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

The given equations are x + 3y - 2 and 2x - y + 5.
Here,  and 
Now, 
Clearly, 
Therefore, the graph lines of the equations will intersect at a point.

What will be the nature of the graph lines of the equations x + 3y - 2 and 2x - y + 5?

MathematicsGrade-8

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

The given equations are x + 3y - 2 and 2x - y + 5.
Here,  and 
Now, 
Clearly, 
Therefore, the graph lines of the equations will intersect at a point.

Mathematics

What will be the nature of the graph lines of the equations 5x - 2y + 9 and 15x - 6y + 1?

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

The given equations are 5x - 2y + 9 and 15x - 6y + 1.
Here,  and 
Now, 
Clearly, 
Therefore, the graph lines of the equations will be parallel.

What will be the nature of the graph lines of the equations 5x - 2y + 9 and 15x - 6y + 1?

MathematicsGrade-8

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

The given equations are 5x - 2y + 9 and 15x - 6y + 1.
Here,  and 
Now, 
Clearly, 
Therefore, the graph lines of the equations will be parallel.

Mathematics

What is the y intercept in the equation y = x + 5?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope.
The equation y = mx + b is the equation of line, where:
m= slope of the equation
b= y-intercept
Now we have given the equation as: y = x + 5
Comparing it, we get:
m= 1
b= 5
So the y intercept of the given equation is 5.

What is the y intercept in the equation y = x + 5?

MathematicsGrade-8

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope.
The equation y = mx + b is the equation of line, where:
m= slope of the equation
b= y-intercept
Now we have given the equation as: y = x + 5
Comparing it, we get:
m= 1
b= 5
So the y intercept of the given equation is 5.

Mathematics

What is the graphical representation of the following equations?3x + 6y = 3900 and x + 2y = 1300

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

Now we have given the equations as:

Comparing it, we get:

So it shows that the lines are coinciding lines and an infinite number of solutions.

What is the graphical representation of the following equations?3x + 6y = 3900 and x + 2y = 1300

MathematicsGrade-8

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

Now we have given the equations as:

Comparing it, we get:

So it shows that the lines are coinciding lines and an infinite number of solutions.

Mathematics

What is the graphical representation of the following equations?x + 2y = 30 and 2x + 4y = 66

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

Now we have given the equations as:

Comparing it, we get:

So it shows that the lines are parallel lines and have no solution.

What is the graphical representation of the following equations?x + 2y = 30 and 2x + 4y = 66

MathematicsGrade-8

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

Now we have given the equations as:

Comparing it, we get:

So it shows that the lines are parallel lines and have no solution.

Mathematics

What is the graphical representation of the following equations?3x + 2y = 80   and 4x + 3y = 110

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

Now we have given the equations as:

Comparing it, we get:

So it shows that the lines are intersecting lines and has 1 solution.

What is the graphical representation of the following equations?3x + 2y = 80   and 4x + 3y = 110

MathematicsGrade-8

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.

There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.

When the lines are coinciding with each other then there is infinite number of solutions.

Now we have given the equations as:

Comparing it, we get:

So it shows that the lines are intersecting lines and has 1 solution.

Mathematics

If a linear equation has one variable, what is it called?

An equation that has two variables and the highest power of the variables is 1 is called linear equation in two variables.
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+7=0 only has one variable.
The following procedures are used to solve an equation with a single variable.
Clear any fractions using the LCM in step one.
Simple all sides of the equation in step two.
Isolate the variable in step three.
Finally, check your response.
So the answer is a Linear equation in one variable.

If a linear equation has one variable, what is it called?

MathematicsGrade-8

An equation that has two variables and the highest power of the variables is 1 is called linear equation in two variables.
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+7=0 only has one variable.
The following procedures are used to solve an equation with a single variable.
Clear any fractions using the LCM in step one.
Simple all sides of the equation in step two.
Isolate the variable in step three.
Finally, check your response.
So the answer is a Linear equation in one variable.

Mathematics

If a linear equation has two variables, what is it called?

An equation that has two variables and the highest power of the variables is 1 is called linear equation in two variables.
The expression for a linear equation involving two variables is Ax + by + C = 0, where A, B, and C are constants and x and y are the two variables, each with a degree of one.
In this there are three systems:

• No solution: Parallel lines
• One solution: Intersecting lines
• Infinitely many solutions: Coincident lines

So the answer is Linear equation in two variables.

If a linear equation has two variables, what is it called?

MathematicsGrade-8

An equation that has two variables and the highest power of the variables is 1 is called linear equation in two variables.
The expression for a linear equation involving two variables is Ax + by + C = 0, where A, B, and C are constants and x and y are the two variables, each with a degree of one.
In this there are three systems:

• No solution: Parallel lines
• One solution: Intersecting lines
• Infinitely many solutions: Coincident lines

So the answer is Linear equation in two variables.

Mathematics

What is the point of intersection of the line with the coordinate axes?

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.
There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.
When the lines are coinciding with each other then there is infinite number of solutions.
Origin is the coordinate axis' place of intersection (0,0). The horizontal and vertical axes are the two axes of the coordinate plane.
The origin is defined as the point of intersection (0, 0). The x-coordinate is always listed first and the y-coordinate is always listed second in an ordered pair. The intersection of the x and y axes is at zero on both axes. A point in quadrant I, has a positive x and y coordinate value since the x and y axes both meet at zero, for instance (1,1).

What is the point of intersection of the line with the coordinate axes?

MathematicsGrade-8

The value or values that hold true for each equation in the system constitute the solution to the system of equations. How many solutions there are for a system can be determined from the graphs of its equations.
If the point of intersection is the only location where the two graphs meet when the lines cross, the coordinates of that location provide the answer to the equations involving the two variables.
There are no solutions when the lines are parallel. There are always infinitely many solutions when the two equations graph as the same line.
When the lines are coinciding with each other then there is infinite number of solutions.
Origin is the coordinate axis' place of intersection (0,0). The horizontal and vertical axes are the two axes of the coordinate plane.
The origin is defined as the point of intersection (0, 0). The x-coordinate is always listed first and the y-coordinate is always listed second in an ordered pair. The intersection of the x and y axes is at zero on both axes. A point in quadrant I, has a positive x and y coordinate value since the x and y axes both meet at zero, for instance (1,1).

For what value of k do the equations represent coincident lines?

Do the equations 2x 3y 1 and 6y 4x 2 represent a pair of coincident lines justify your answer?

How do you find the value of k in a linear equation?

For what value of k the pair of linear equations 4x 6y 2 and 2x KY 3 does not have a solution?