In both systems, we can use the method of elimination to find the value of c that would give the same solution.
For the first system:
Multiply the first equation by 2:
8x + 2y = -2
This matches the second equation of the second system, so c would need to be 2 to get the same solution for both systems.
Therefore, the value of c that would give the same solution for both systems is 2.
Two systems of equations are shown:%0D%0A%0D%0A4x+y=−1%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A−%0D%0A1%0D%0Ax+y=2%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A2%0D%0Aand%0D%0A%0D%0A8x+2y=−2%0D%0A8%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A2%0D%0A−4x+cy=−8%0D%0A−%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A%0D%0A=%0D%0A−%0D%0A8%0D%0AWhat would the value of c need to be to get the same solution for both systems?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A2%0D%0A2%0D%0A%0D%0A1%0D%0A1%0D%0A%0D%0A-4%0D%0A-4%0D%0A%0D%0A4%0D%0A4%0D%0A%0D%0A-2
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