Two systems of equations are shown:

Question

4x+y=−1
x+y=2

8x+2y=−2
−4x+cy=−8
What would the value of c in the second system need to be to get the same solution for both systems?

Answer 1

To find the value of c that will give the same solution for both systems, we can compare the equations of the two systems.

In the first system, we have:

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

In the second system, we have:

8x + 2y = -2 ...(Equation 3)
-4x + cy = -8 ...(Equation 4)

To solve for the same solution in both systems, the coefficients of x and y in the respective equations should be the same.

Comparing the coefficients in Equation 1 and Equation 3:

4x = 8x
This implies that 4 = 8, which is not true. Therefore, we cannot find a value of c that will make the two systems have the same solution.