Question

use elimination to solve the system of equations.
11f + 14g = 13
11f + 10g = 25
(\boxed{ }, \boxed{ })

Explanation:

Step1: Subtract the two equations

Subtract the second equation from the first to eliminate \(11f\).
\((11f + 14g)-(11f + 10g)=13 - 25\)
Simplify the left - hand side: \(11f+14g - 11f - 10g=4g\)
Simplify the right - hand side: \(13 - 25=-12\)
So we get the equation \(4g=-12\)

Step2: Solve for \(g\)

Divide both sides of the equation \(4g = - 12\) by 4.
\(g=\frac{-12}{4}=-3\)

Step3: Substitute \(g = - 3\) into one of the original equations

Substitute \(g=-3\) into the first original equation \(11f + 14g=13\).
We have \(11f+14\times(-3)=13\)
First, calculate \(14\times(-3)=-42\)
So the equation becomes \(11f-42 = 13\)
Add 42 to both sides: \(11f=13 + 42\)
\(11f=55\)
Divide both sides by 11: \(f = 5\)

Answer:

\((5,-3)\)