Question

5 5x + y = 2 5x - 3y = 14

Explanation:

Step1: Label the equations

Let
$5x + y = 2$ --- Equation (1)
$5x - 3y = 14$ --- Equation (2)

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

Subtract to eliminate $5x$:
$$(5x + y) - (5x - 3y) = 2 - 14$$
$$5x + y - 5x + 3y = -12$$
$$4y = -12$$

Step3: Solve for $y$

Divide both sides by 4:
$$y = \frac{-12}{4} = -3$$

Step4: Substitute $y=-3$ into Eq(1)

Find value of $x$:
$$5x + (-3) = 2$$
$$5x - 3 = 2$$

Step5: Solve for $x$

Add 3 to both sides, then divide by 5:
$$5x = 2 + 3 = 5$$
$$x = \frac{5}{5} = 1$$

Answer:

$x=1$, $y=-3$