Question

use elimination to solve the system of equations. enter your answers in the boxes.
$3x - 2y = 24$
$x + 2y = 48$
$x = \boxed{}$ ; $y = \boxed{}$

Explanation:

Step1: Add the two equations

We have the system:

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Adding the two equations together to eliminate \(y\):
\((3x - 2y)+(x + 2y)=24 + 48\)
Simplifying the left side: \(3x - 2y+x + 2y = 4x\)
Simplifying the right side: \(24+48 = 72\)
So we get \(4x=72\)

Step2: Solve for \(x\)

Divide both sides of \(4x = 72\) by 4:
\(x=\frac{72}{4}=18\)

Step3: Substitute \(x = 18\) into one of the original equations

Let's use the second equation \(x + 2y=48\). Substitute \(x = 18\) into it:
\(18+2y=48\)
Subtract 18 from both sides: \(2y=48 - 18=30\)
Divide both sides by 2: \(y=\frac{30}{2}=15\)

Answer:

\(x = 18\); \(y = 15\)