To find the value of c that would give the same solution for both systems of equations, we need to solve the systems and compare the values of y in each system.
For the first system:
4x + y = -1
x + y = 2
Rearranging the second equation, we get:
y = 2 - x
Substituting this value into the first equation, we have:
4x + (2 - x) = -1
Simplifying, we get:
3x + 2 = -1
3x = -3
x = -1
Substituting x = -1 into the second equation, we have:
y = 2 - (-1)
y = 2 + 1
y = 3
Therefore, the solution for the first system is (-1, 3).
For the second system:
8x + 2y = -2
-4x + cy = -8
We need to find the value of c that would make the y-values in both systems equal. From the first system, we know that y = 3. Substituting y = 3 into the second equation, we have:
-4x + 3c = -8
Simplifying, we get:
4x - 3c = 8
Comparing this equation with the first equation in the second system, which is 8x + 2y = -2, we can see that the coefficient of y in both equations must be the same. Therefore, we need to find the value of c that would make the coefficient of y in the second equation equal to 2.
From the equation 4x - 3c = 8, we can see that -3c = 2 when c = -4.
Therefore, the value of c that would give the same solution for both systems is -4.
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
-4
-4
1
1
4
4
2
2
-2
2 answers
its -4 I think