Question

find the solution of the system of equations.
$3x - 8y = 19$
$3x + 5y = -46$

Explanation:

Step1: Subtract equations to eliminate $x$

$(3x - 8y) - (3x + 5y) = 19 - (-46)$
Simplify: $3x -8y -3x -5y = 19 + 46$
$-13y = 65$

Step2: Solve for $y$

$y = \frac{65}{-13}$
$y = -5$

Step3: Substitute $y=-5$ into first equation

$3x - 8(-5) = 19$
$3x + 40 = 19$

Step4: Solve for $x$

$3x = 19 - 40$
$3x = -21$
$x = \frac{-21}{3}$
$x = -7$

Answer:

$x=-7$, $y=-5$