Question

② -9x + 3y = 27
-3x + 4y = 27

Explanation:

Step1: Eliminate x variable

Multiply the second equation by 3:
$$3(-3x + 4y) = 3(27)$$
$$-9x + 12y = 81$$

Step2: Subtract first equation

Subtract $-9x + 3y = 27$ from the new equation:
$$(-9x + 12y) - (-9x + 3y) = 81 - 27$$
$$9y = 54$$

Step3: Solve for y

Divide both sides by 9:
$$y = \frac{54}{9} = 6$$

Step4: Substitute y into second equation

Plug $y=6$ into $-3x + 4y = 27$:
$$-3x + 4(6) = 27$$
$$-3x + 24 = 27$$

Step5: Solve for x

Isolate x:
$$-3x = 27 - 24$$
$$-3x = 3$$
$$x = \frac{3}{-3} = -1$$

Answer:

$x=-1$, $y=6$