Question

Solve the following system by elimination. Show work and explain each step. $3x + y = 13 \\ 4x - 3y = 13$

Answer 1

There are two equations given 3x + y = 13 and 4x - 3y = 13.

Multiply the first equation by 3 to get 9x + 3y = 39 and add it to second equation.

$\begin{gathered} 9x+3y+4x-3y=39+13 \\ \Rightarrow13x=52 \\ \Rightarrow\frac{13x}{13}=\frac{52}{13} \\ \Rightarrow x=4 \end{gathered}$

Substitute x = 4, in first equation to find y,

$\begin{gathered} 3(4)+y=13 \\ \Rightarrow12+y=13 \\ \Rightarrow y=13-12 \\ \Rightarrow y=1 \end{gathered}$