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 same solution for both systems of equations, the determinants of the coefficient matrices must be equal.

For the first system:

Coefficient matrix A = [[4, 1], [1, 1]]
Determinant of A = 4(1) - 1(1) = 4 - 1 = 3

For the second system:

Coefficient matrix B = [[8, 2], [-4, c]]
Determinant of B = 8(c) - 2(-4) = 8c + 8

To find the value of c that makes the determinants equal, set them equal to each other and solve for c:

3 = 8c + 8
8c = 3 - 8
8c = -5
c = -5/8

Therefore, the value of c that would make the determinants equal and give the same solution for both systems is -5/8.