Given the System of Equations:
[tex]\begin{cases}y=x+7 \\ \\ y=\frac{1}{4}x+\frac{11}{2}\end{cases}[/tex]You can apply the following steps in order to solve it using the Substitution Method:
1. Substitute the second equation into the first equation:
[tex]\frac{1}{4}x+\frac{11}{2}=x+7[/tex]2. Solve for "x":
[tex]\begin{gathered} \frac{1}{4}x-x=7-\frac{11}{2} \\ \\ -\frac{3}{4}x=\frac{3}{2} \end{gathered}[/tex][tex]\begin{gathered} x=(\frac{3}{2})(-\frac{4}{3}) \\ \\ x=-\frac{12}{6} \\ \\ x=-2 \end{gathered}[/tex]3. You can substitute the value of "x" into the first original equation:
[tex]\begin{gathered} y=x+7 \\ y=(-2)+7 \end{gathered}[/tex]4. Evaluating, you get this value of "y":
[tex]\begin{gathered} y=-2+7 \\ y=5 \end{gathered}[/tex]Hence, the answer is: First option.