Question

1. $-6x + 3y = -24$ $-3x + 10y = 22$

Explanation:

Step 1: Eliminate x by multiplying the second equation

Multiply the second equation \(-3x + 10y = 22\) by 2 to get \(-6x + 20y = 44\).
$$-3x\times2 + 10y\times2 = 22\times2 \implies -6x + 20y = 44$$

Step 2: Subtract the first equation from the new equation

Subtract \(-6x + 3y = -24\) from \(-6x + 20y = 44\):
$$(-6x + 20y) - (-6x + 3y) = 44 - (-24)$$
$$-6x + 20y + 6x - 3y = 44 + 24$$
$$17y = 68$$

Step 3: Solve for y

Divide both sides by 17:
$$y = \frac{68}{17} = 4$$

Step 4: Substitute y into one of the original equations to find x

Use the first equation \(-6x + 3y = -24\). Substitute \(y = 4\):
$$-6x + 3\times4 = -24$$
$$-6x + 12 = -24$$

Step 5: Solve for x

Subtract 12 from both sides:
$$-6x = -24 - 12 = -36$$
Divide both sides by -6:
$$x = \frac{-36}{-6} = 6$$

Answer:

\(x = 6\), \(y = 4\)