Question

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$$\begin{cases} 3x = 2y - 7 \\\\ 2x - 5y = 10 \\end{cases}$$

Explanation:

Step1: Rewrite first equation

$3x - 2y = -7$

Step2: Scale equations for elimination

Multiply Step1 by 2: $6x - 4y = -14$
Multiply second equation by 3: $6x - 15y = 30$

Step3: Subtract equations to eliminate $x$

$(6x - 4y) - (6x - 15y) = -14 - 30$
$11y = -44$

Step4: Solve for $y$

$y = \frac{-44}{11} = -4$

Step5: Substitute $y$ into second equation

$2x - 5(-4) = 10$
$2x + 20 = 10$

Step6: Solve for $x$

$2x = 10 - 20 = -10$
$x = \frac{-10}{2} = -5$

Answer:

$x=-5$, $y=-4$