Question

1. 2x + y = 20

6x - 5y = 12

Explanation:

Step1: Eliminate x via scaling

Multiply first equation by 3:
$$3(2x + y) = 3 \times 20$$
$$6x + 3y = 60$$

Step2: Subtract second equation

Subtract $6x - 5y = 12$ from the new equation:
$$(6x + 3y) - (6x - 5y) = 60 - 12$$
$$8y = 48$$

Step3: Solve for y

Divide both sides by 8:
$$y = \frac{48}{8} = 6$$

Step4: Substitute y into first equation

Plug $y=6$ into $2x + y = 20$:
$$2x + 6 = 20$$
$$2x = 20 - 6 = 14$$

Step5: Solve for x

Divide both sides by 2:
$$x = \frac{14}{2} = 7$$

Answer:

$x=7$, $y=6$