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.

false

step-by-step explanation:

4y - 6 + 4y^2 - 9

before simplifying this contains 4 terms

after simplifying

4y -15 + 4y^2

it contains 3 terms