To solve this system of linear equations using the elimination method, first, add both equations:
[tex]\begin{gathered} 8x+5y=38\Rightarrow\text{ Equation 1} \\ -8x+2y=4\Rightarrow\text{ Equation 2} \end{gathered}[/tex][tex]\begin{gathered} 8x+5y=38 \\ -8x+2y=4\text{ +} \\ --------- \\ 0x+7y=42 \\ 7y=42 \end{gathered}[/tex]
Now solve for y dividing by 7 on both sides of the equation:
[tex]\begin{gathered} \frac{7y}{7}=\frac{42}{7} \\ y=6 \end{gathered}[/tex]
Finally, replace the value of y in any of the initial equations, for example in equation 1
[tex]\begin{gathered} 8x+5y=38 \\ 8x+5(6)=38 \\ 8x+30=38 \\ \text{ Subtract 30 from both sides of the equation} \\ 8x+30-30=38-30 \\ 8x=8 \\ \text{ Divide by 8 from both sides of the equation} \\ \frac{8x}{8}=\frac{8}{8} \\ x=1 \end{gathered}[/tex]
Therefore, the solution of the system of equations is
[tex]\begin{cases}x=1 \\ y=6\end{cases}[/tex]
