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 the second equation

We have the second equation \( \frac{x}{2}+2y = 6 \). Substitute \( x = y - 3 \) into it:
\( \frac{y - 3}{2}+2y = 6 \)

Step2: Solve for \( y \)

Multiply through by 2 to eliminate the fraction:
\( y - 3 + 4y = 12 \)
Combine like terms:
\( 5y - 3 = 12 \)
Add 3 to both sides:
\( 5y = 15 \)
Divide both sides by 5:
\( y = 3 \)

Step3: Find \( x \) using \( x = y - 3 \)

Substitute \( y = 3 \) into \( x = y - 3 \):
\( x = 3 - 3 = 0 \)
So the ordered pair is \( (0, 3) \).

Answer:

B) \( (0, 3) \)