Let's solve the system
[tex]\begin{cases}6x+8y=106 \\ 5x-4y=3\end{cases}[/tex]
First, multiply equation 2 by 2
[tex]\begin{cases}6x+8y=106 \\ 5x-4y=3\end{cases}\rightarrow\begin{cases}6x+8y=106 \\ 10x-8y=6\end{cases}[/tex]
Then, add up equations 1 and 2
[tex]\begin{cases}6x+8y=106 \\ 10x-8y=6\end{cases}\rightarrow16x=112[/tex]
Solve for x :
[tex]16x=112\rightarrow x=\frac{112}{16}\Rightarrow x=7[/tex]
Substitute in equation 1 and solve for y :
[tex]\begin{gathered} 6x+8y=106 \\ \rightarrow6(7)+8y=106 \\ \rightarrow8y=106-6(7) \\ \rightarrow8y=64\rightarrow y=\frac{64}{8}\Rightarrow y=8 \end{gathered}[/tex]
This way, we get that:
[tex]\begin{gathered} x=7 \\ y=8 \end{gathered}[/tex]
