Question

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?
2,1,-2,4,-4

Answer 1

To find the value of c that would give the same solution for both systems of equations, we can solve both systems and then compare the solutions.

For the first system:
4x + y = -1
x + y = 2

We can solve this system by elimination. By subtracting the second equation from the first equation, we get:

4x + y - (x + y) = -1 - 2
3x = -3
x = -1

Plugging this value back into the second equation, we get:

-1 + y = 2
y = 3

So the solution for the first system is x = -1 and y = 3.

For the second system:
8x + 2y = -2
-4x + cy = -8

Similarly, we can solve this system by elimination. By multiplying the first equation by -2 and adding it to the second equation, we get:

-16x - 4y + cy = 4 + (-8)
(-16 + c)x - 4y = -4
12x - 4y = -4

Comparing this equation to the first equation of the first system, we can see that for both systems to have the same solution, the coefficients of x and y should be the same. Thus, we can set up the equation:

12 = 4
c = 4/4
c = 1

Therefore, the value of c that would give the same solution for both systems is 1.