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?
2
-2
4
-4
1
pls what is the correct answer i see several different ones
To find the value of c that would give the same solution for both systems, we can compare the slopes of the two equations.
For the first system, the slope is -4 (since it is in the form y = mx + b).
For the second system, the slope is -4x / -8 = 1/2.
To get the same solution for both systems, the slopes must be equal to each other. Therefore, we need to find the value of c in the second system such that the slope is -4.
Given that -4x / -8 = 1/2, we can solve for c as follows:
-4 = 1/2
-4 * (-8) = c * (-8)
32 = -8c
c = -4
So the correct answer is c = -4.
the slopes have nothing to do with the solutions.
The first system has solution (-1,3)
For this to be a solution of
8x+2y=−2
−4x+cy=−8
we need c = -4
Apologies for the confusion caused in my previous response. You are correct.
The first system has a solution of (-1, 3). To find the value of c that would give the same solution for both systems, we substitute (-1, 3) into the second system:
For the first equation of the second system, 8(-1) + 2(3) = -2, which is true.
For the second equation of the second system, -4(-1) + c(3) = -8. Simplifying this equation gives c = -4.
Therefore, the correct value of c that would make both systems have the same solution is c = -4.