Question

use the elimination method to solve the system of equations. choose the correct ordered pair.
3x + 5y = 48
-3x + 5y = 12

a. (16, 0)
b. (-4, 0)
c. (6, 6)
d. (-3, 5)

Explanation:

Step1: Eliminate \(x\) by adding equations

Add the two equations \(3x + 5y = 48\) and \(-3x + 5y = 12\) together.
\((3x + 5y)+(-3x + 5y)=48 + 12\)
Simplify left side: \(3x-3x + 5y+5y = 10y\), right side: \(60\). So \(10y=60\).

Step2: Solve for \(y\)

Divide both sides of \(10y = 60\) by \(10\): \(y=\frac{60}{10}=6\).

Step3: Substitute \(y = 6\) to find \(x\)

Substitute \(y = 6\) into the first equation \(3x+5y = 48\): \(3x+5\times6 = 48\).
Simplify: \(3x + 30 = 48\). Subtract \(30\) from both sides: \(3x=48 - 30=18\).
Divide by \(3\): \(x=\frac{18}{3}=6\).

Answer:

C. \((6,6)\)