Question

4 6x - 2y = 10; x - 2y = -5

Explanation:

Step1: Label the equations

Let:
$$6x - 2y = 10 \tag{1}$$
$$x - 2y = -5 \tag{2}$$

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

Eliminate $-2y$ by subtraction:
$$(6x - 2y) - (x - 2y) = 10 - (-5)$$
$$6x - 2y - x + 2y = 15$$
$$5x = 15$$

Step3: Solve for x

Divide both sides by 5:
$$x = \frac{15}{5} = 3$$

Step4: Substitute x=3 into eq(2)

Find the value of y:
$$3 - 2y = -5$$
$$-2y = -5 - 3$$
$$-2y = -8$$

Step5: Solve for y

Divide both sides by -2:
$$y = \frac{-8}{-2} = 4$$

Answer:

$x=3$, $y=4$