Question

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$$\begin{cases} 2x + 3y = 13 \\\\ 6 + 2y = -5x \\end{cases}$$

Explanation:

Step1: Rewrite second equation

Rearrange into standard form.
$5x + 2y = -6$

Step2: Set up system

Define the linear system clearly:

$$\begin{cases} 2x + 3y = 13 \\ 5x + 2y = -6 \end{cases}$$

Step3: Eliminate $y$ variable

Multiply equations to match $y$ coefficients:

• Multiply first eq by 2: $4x + 6y = 26$
• Multiply second eq by 3: $15x + 6y = -18$

Subtract first new eq from second:
$15x + 6y - (4x + 6y) = -18 - 26$
$11x = -44$

Step4: Solve for $x$

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

Step5: Solve for $y$

Substitute $x=-4$ into $2x + 3y =13$:
$2(-4) + 3y = 13$
$-8 + 3y = 13$
$3y = 13 + 8 = 21$
$y = \frac{21}{3} = 7$

Answer:

$x=-4$, $y=7$