Question

8.
$2x + 3y = 7$
$3x - 6y = 21$

Explanation:

Step1: Eliminate y via scaling Eq1

Multiply first equation by 2:
$$2(2x + 3y) = 2 \times 7$$
$$4x + 6y = 14$$

Step2: Add to Eq2 to solve for x

Add the new equation to the second equation:
$$(4x + 6y) + (3x - 6y) = 14 + 21$$
$$7x = 35$$
$$x = \frac{35}{7} = 5$$

Step3: Substitute x into Eq1 for y

Plug $x=5$ into $2x + 3y = 7$:
$$2(5) + 3y = 7$$
$$10 + 3y = 7$$
$$3y = 7 - 10 = -3$$
$$y = \frac{-3}{3} = -1$$

Answer:

$x=5$, $y=-1$