Question

1. $6x - 2y = 1$ $10x - 2y = 5$

Explanation:

Step1: Label the equations

Let
$6x - 2y = 1$ --- Equation (1)
$10x - 2y = 5$ --- Equation (2)

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

Subtract to eliminate $-2y$:
$$(10x - 2y) - (6x - 2y) = 5 - 1$$
$$10x - 2y - 6x + 2y = 4$$
$$4x = 4$$

Step3: Solve for $x$

Divide both sides by 4:
$$x = \frac{4}{4} = 1$$

Step4: Substitute $x=1$ into Eq(1)

Find the value of $y$:
$$6(1) - 2y = 1$$
$$6 - 2y = 1$$

Step5: Solve for $y$

Rearrange and isolate $y$:
$$-2y = 1 - 6$$
$$-2y = -5$$
$$y = \frac{-5}{-2} = \frac{5}{2}$$

Answer:

$x=1$, $y=\frac{5}{2}$