Question

1. $7x + 4y = 2$

$7x + 2y = 8$

Explanation:

Step1: Label the equations

Let
$$7x + 4y = 2 \tag{1}$$
$$7x + 2y = 8 \tag{2}$$

Step2: Subtract eq(2) from eq(1)

Eliminate $7x$ by subtraction:
$$(7x + 4y) - (7x + 2y) = 2 - 8$$
$$2y = -6$$

Step3: Solve for $y$

Divide both sides by 2:
$$y = \frac{-6}{2} = -3$$

Step4: Substitute $y=-3$ into eq(2)

Plug $y$ value to find $x$:
$$7x + 2(-3) = 8$$
$$7x - 6 = 8$$

Step5: Solve for $x$

Isolate $x$ by first adding 6 to both sides:
$$7x = 8 + 6 = 14$$
Then divide by 7:
$$x = \frac{14}{7} = 2$$

Answer:

$x=2$, $y=-3$