Question

find the solution of the system of equations.
$8x - 3y = 2$
$-8x - 5y = 46$

Explanation:

Step1: Add the two equations

$$\begin{align*} (8x - 3y) + (-8x - 5y) &= 2 + 46 \\ 8x - 3y -8x -5y &= 48 \\ -8y &= 48 \end{align*}$$

Step2: Solve for $y$

$y = \frac{48}{-8} = -6$

Step3: Substitute $y=-6$ into first equation

$8x - 3(-6) = 2$
$8x + 18 = 2$

Step4: Solve for $x$

$8x = 2 - 18 = -16$
$x = \frac{-16}{8} = -2$

Answer:

$x=-2$, $y=-6$