Question

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$$\begin{cases} 4x + 3y = -1 \\\\ 5x + 4y = 1 \\end{cases}$$

Explanation:

Step1: Eliminate x via scaling equations

Multiply first eq by 5: $20x + 15y = -5$
Multiply second eq by 4: $20x + 16y = 4$

Step2: Subtract scaled equations

Subtract first scaled eq from second:
$(20x + 16y) - (20x + 15y) = 4 - (-5)$
$y = 9$

Step3: Substitute y into first equation

Plug $y=9$ into $4x + 3y = -1$:
$4x + 3(9) = -1$
$4x + 27 = -1$

Step4: Solve for x

Isolate x:
$4x = -1 - 27$
$4x = -28$
$x = \frac{-28}{4} = -7$

Answer:

$x = -7$, $y = 9$