Question

3
$x = y - 3$
$\frac{x}{2} + 2y = 6$
which ordered pair $(x, y)$ satisfies the system of equations shown above?
a) $(-3, 0)$
b) $(0, 3)$
c) $(6, -3)$
d) $(36, -6)$

Explanation:

Step1: Substitute $x=y-3$ into second equation

$\frac{y-3}{2} + 2y = 6$

Step2: Eliminate denominator, multiply by 2

$y-3 + 4y = 12$

Step3: Combine like terms

$5y - 3 = 12$

Step4: Solve for $y$

$5y=15 \implies y=3$

Step5: Substitute $y=3$ into $x=y-3$

$x=3-3=0$

Answer:

B) (0, 3)