Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = -2x + 4 6x + 3y = -12 -4 4 12

This question is based on system of linear equation .Thus, for a=12 will have infinitely many solution.

Given:

y = -2x + 4 ------ (a)  

6x + 3y = a ------(b)

We need to determined the value of a for which the system gives infinitely many solution.

Now check all the options as given below:

Option(1)  a = -12 and put it in (b) we get,

6x + 3y = -12

 2x + y = -4

y = -2x - 4

Both the equations have same slope, therefore, they are parallel to each other and have no solutions.

Option(2)  a= -4 and put it in (b) we get,

6x + 3y = -4

3y = -6x - 4

Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.

Option(3) a= 4

6x + 3y = 4

3y = -6x + 4

Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.

Option(4) a= 12

6x + 3y = 12

3y = -6x + 12

y = -2x + 4

Both the  equation are same for a= 12.

Thus, for a=12 will have infinitely many solution.

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Option (4)

Step-by-step explanation:

The given system of equations is,

y = -2x + 4 ------ (1)

6x + 3y = a --------(2)

We have to find the value of a for which the system of equations will have infinitely many solutions.

Option (1). If a = -12

                6x + 3y = -12

                2x + y = -4

                        y = -2x - 4

Both the equations have same slope, therefore, they are parallel and will have no solutions.

Option (2). If a = -4

                 6x + 3y = -4

                         3y = -6x - 4

Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.

Option (3). If a = 4

                 6x + 3y = 4

                         3y = -6x + 4

                           y = -2x +

Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.

Option (4). If a = 12

                  6x + 3y = 12

                           3y = -6x + 12

                             y = -2x + 4

Therefore, both the equations (1) and (2) are same for a = 12 and they will have infinitely many solutions.

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step-by-step explanation: