Question

find the solution of the system of equations.
$3x - y = 19$
$3x - 4y = -5$

Explanation:

Step1: Label the equations

Let
$3x - y = 19$ --- Equation (1)
$3x - 4y = -5$ --- Equation (2)

Step2: Subtract Equation (2) from (1)

Subtract to eliminate $3x$:
$$(3x - y) - (3x - 4y) = 19 - (-5)$$
$$3x - y - 3x + 4y = 19 + 5$$
$$3y = 24$$

Step3: Solve for $y$

Divide both sides by 3:
$$y = \frac{24}{3} = 8$$

Step4: Substitute $y=8$ into Equation (1)

Find value of $x$:
$$3x - 8 = 19$$
$$3x = 19 + 8 = 27$$

Step5: Solve for $x$

Divide both sides by 3:
$$x = \frac{27}{3} = 9$$

Answer:

$x=9$, $y=8$