Question

solve the system of equations $5x - 8y = -18$ and $-4x + 3y = -6$ by combining the equations.
$\square\\ (5x\\ \\ \\ -8y\\ \\ =-18)$
$\square\\ (-4x\\ +3y\\ \\ = -6)$
$\

$$\begin{align*}5x\\ -8y\\ \\ &= -18\\\\-4x\\ +3y\\ \\ &= -6\\\\\\hline\\square\\ x + \\square\\ y=\\ \\square\\end{align*}$$

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Explanation:

Step1: Eliminate x variable

Multiply first equation by 4: $4(5x - 8y) = 4(-18) \implies 20x - 32y = -72$
Multiply second equation by 5: $5(-4x + 3y) = 5(-6) \implies -20x + 15y = -30$

Step2: Add the two new equations

Add to cancel $x$: $(20x - 32y) + (-20x + 15y) = -72 + (-30)$
Simplify: $-17y = -102$

Step3: Solve for y

Isolate y: $y = \frac{-102}{-17} = 6$

Step4: Substitute y=6 into first equation

Substitute into $5x - 8y = -18$: $5x - 8(6) = -18$
Simplify: $5x - 48 = -18$

Step5: Solve for x

Isolate x: $5x = -18 + 48 = 30$
$x = \frac{30}{5} = 6$

Answer:

$x=6$, $y=6$

For the blanks in the given template:

To eliminate $x$, fill the first box with 4 and the second box with 5. Adding the scaled equations gives:
$0x + (-17)y = -102$
Then solve to get $x=6$, $y=6$