Two systems of equations are shown: 4x+y=−1 x+y=2 and 8x+2y=−2 −4x+cy=−8 What would the value of c need to be to get the same solution for both systems? (1 point) Responses -2 -2 1 1 2 2 4 4 -4
To determine the value of c that would give the same solution for both systems, we need to compare the slopes of the two equations in each system.
For the first system,
4x+y=-1 -> y = -4x-1
x+y=2 -> y = -x+2
The slopes of these two equations are -4 and -1, respectively.
For the second system,
8x+2y=-2 -> y = -4x-1
-4x+cy=-8 -> y = cx+2
The slopes of these two equations are also -4 and c, respectively.
In order for the systems to have the same solution, the slopes of the second system need to be equal to the slopes of the first system. Therefore, c needs to be equal to -4.
Answer: -4