Question

1. $-2x + y = 12$

$3x + 3y = 9$

Explanation:

Step1: Simplify the second equation

Divide the second equation by 3:
$$\frac{3x+3y}{3}=\frac{9}{3}$$
$$x + y = 3$$
Rearrange to isolate $y$:
$$y = 3 - x$$

Step2: Substitute $y$ into first equation

Substitute $y=3-x$ into $-2x + y = 12$:
$$-2x + (3 - x) = 12$$
Combine like terms:
$$-3x + 3 = 12$$

Step3: Solve for $x$

Subtract 3 from both sides:
$$-3x = 12 - 3$$
$$-3x = 9$$
Divide by -3:
$$x = \frac{9}{-3} = -3$$

Step4: Solve for $y$

Substitute $x=-3$ into $y=3-x$:
$$y = 3 - (-3) = 6$$

Answer:

$x=-3$, $y=6$