Question

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: Find $x$ using $x=y-3$

$x=3-3=0$

Answer:

B) (0, 3)