Question

1. find the solution of the system of equations.

$2x - 3y = -14$
$5x + 9y = -2$

Explanation:

Step1: Eliminate $y$ variable

Multiply first equation by 3:
$3(2x - 3y) = 3(-14)$
$\implies 6x - 9y = -42$

Step2: Add to second equation

Add new equation to $5x + 9y = -2$:
$(6x - 9y) + (5x + 9y) = -42 + (-2)$
$\implies 11x = -44$

Step3: Solve for $x$

Divide both sides by 11:
$x = \frac{-44}{11} = -4$

Step4: Substitute $x=-4$ to find $y$

Use first equation $2x - 3y = -14$:
$2(-4) - 3y = -14$
$\implies -8 - 3y = -14$
$\implies -3y = -14 + 8 = -6$
$\implies y = \frac{-6}{-3} = 2$

Answer:

$x=-4$, $y=2$ (or the ordered pair $(-4, 2)$)