Suppose a, b, c, and d are constants such that a is not zero and the system below is consistent for all possible values of f and g. what can you say about the numbers a, b, c, and d?

[tex]ax_1+bx_2=f\\cx_1+dx_2=g[/te x]

ad − bc ≠ 0

Step-by-step explanation:

If we write this system in matrix form:

"Consistent" means there exists a solution for x₁ and x₂.  That means the coefficient matrix must be invertible.  For that to be true, the determinant cannot be 0.

-4

step-by-step explanation:

(-4+8)=-(4-8)=-8+4=-4

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3