Question

Two systems of equations are shown:
4x+y=-1 and x+ y=2
8x+2y=-2 and -4x+cy=-8
What would the value of c need to be to get the same solution for both systems?
A. -2
B. 1
C. -4
D. 4
E. 2

Answer 1

To find the value of c that would result in the same solution for both systems, we can set the two equations in each system equal to each other and solve for c.

For the first system:
4x + y = -1
x + y = 2

Solving for y in terms of x for the first equation, we get:
y = -4x - 1

Substituting this expression for y into the second equation, we get:

x + (-4x - 1) = 2
-3x - 1 = 2
-3x = 3
x = -1

Substituting this value of x back into the first equation, we get:

4(-1) + y = -1
-4 + y = -1
y = 3

So the solution to the first system is (-1, 3).

Now let's consider the second system:
8x + 2y = -2
-4x + cy = -8

Substituting the values of x and y from the first solution into the second system, we get:

8(-1) + 2(3) = -2
-8 + 6 = -2
-2 = -2

This equation is true regardless of the value of c. Therefore, any value of c would result in the same solution for both systems.

The answer is: All values of c would result in the same solution.