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SAT Math Practice Question #30911 - SATify | SATify

#30911

systems

linear equations

hard

90 sec

For a system of two linear equations in two variables, $x$ and $y$ , given by:
$a x + b y d x + ey = c = f$
If the system has infinitely many solutions, which of the following statements must be true?

A.

$a e - b d = 0$ and $a f - c d = 0$

B.

$a = d$ , $b = e$ , and $c = f$

C.

The lines represented by the equations are parallel and distinct.

D.

The ratio $\frac{a}{d}$ is equal to $\frac{b}{e}$ but not equal to $\frac{c}{f}$ .