Question

determine the solution of the system of equations.
$\

$$\begin{cases}2x + 3y = -2\\\\3x - y = 19\\end{cases}$$

$
enter the correct answer in the boxes.
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Explanation:

Step1: Isolate $y$ from second equation

From $3x - y = 19$, rearrange to get:
$y = 3x - 19$

Step2: Substitute $y$ into first equation

Replace $y$ in $2x + 3y = -2$:
$2x + 3(3x - 19) = -2$
Expand and simplify:
$2x + 9x - 57 = -2$
$11x - 57 = -2$

Step3: Solve for $x$

Add 57 to both sides:
$11x = -2 + 57$
$11x = 55$
Divide by 11:
$x = \frac{55}{11} = 5$

Step4: Solve for $y$

Substitute $x=5$ into $y = 3x - 19$:
$y = 3(5) - 19 = 15 - 19 = -4$

Answer:

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