Question

③
-30x + 4y = 2
15x - 12y = -81

Explanation:

Step1: Eliminate x variable

Multiply the second equation by 2:
$$2\times(15x - 12y) = 2\times(-81)$$
$$30x - 24y = -162$$
Add this to the first equation:
$$(-30x + 4y) + (30x - 24y) = 2 + (-162)$$
$$-20y = -160$$

Step2: Solve for y

Divide both sides by -20:
$$y = \frac{-160}{-20} = 8$$

Step3: Substitute y into first equation

Substitute $y=8$ into $-30x + 4y = 2$:
$$-30x + 4\times8 = 2$$
$$-30x + 32 = 2$$

Step4: Solve for x

Isolate x term, then divide:
$$-30x = 2 - 32$$
$$-30x = -30$$
$$x = \frac{-30}{-30} = 1$$

Answer:

$x=1$, $y=8$