Question

solve using elimination.
$x - 5y = -12$
$x + 3y = 20$
( , )
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Explanation:

Step1: Subtract the two equations to eliminate \(x\)

We have the system of equations:
\[

$$\begin{cases} x - 5y = -12 \\ x + 3y = 20 \end{cases}$$

\]
Subtract the first equation from the second equation:
\((x + 3y)-(x - 5y)=20-(-12)\)
Simplify the left - hand side: \(x + 3y - x+5y=8y\)
Simplify the right - hand side: \(20 + 12 = 32\)
So we get the equation \(8y=32\)

Step2: Solve for \(y\)

Divide both sides of the equation \(8y = 32\) by 8:
\(y=\frac{32}{8}=4\)

Step3: Substitute \(y = 4\) into one of the original equations to solve for \(x\)

We substitute \(y = 4\) into the equation \(x+3y = 20\)
\(x+3\times4=20\)
\(x + 12=20\)
Subtract 12 from both sides: \(x=20 - 12=8\)

Answer:

\((8,4)\)