Question

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$$\begin{cases} 5x + 2y = -3 \\\\ 3x + 3y = 9 \\end{cases}$$

Explanation:

Step1: Simplify the second equation

Divide the second equation $3x + 3y = 9$ by 3:
$x + y = 3$, which can be rewritten as $x = 3 - y$

Step2: Substitute $x$ into first equation

Replace $x$ in $5x + 2y = -3$ with $3 - y$:
$5(3 - y) + 2y = -3$
Expand and simplify:
$15 - 5y + 2y = -3$
$15 - 3y = -3$

Step3: Solve for $y$

Rearrange to isolate $-3y$:
$-3y = -3 - 15$
$-3y = -18$
Divide both sides by $-3$:
$y = \frac{-18}{-3} = 6$

Step4: Solve for $x$

Substitute $y = 6$ into $x = 3 - y$:
$x = 3 - 6 = -3$

Answer:

$x = -3$, $y = 6$