To solve the system of equations:
[tex]\begin{gathered} x+\frac{1}{4}y=9 \\ x+y=21 \end{gathered}[/tex]we first notice that both the x coefficients are equal, then we subtract the second equation from the first one to get an equation that only has y as a variable and we solve the resulting equation:
[tex]\begin{gathered} (x+\frac{1}{4}y)-(x+y)=9-21 \\ \frac{1}{4}y-y=-12 \\ -\frac{3}{4}y=-12 \\ y=\frac{-12}{-\frac{3}{4}} \\ y=16 \end{gathered}[/tex]Once we know the value of y we plug it in the first equation and solve for x:
[tex]\begin{gathered} x+\frac{1}{4}(16)=9 \\ x+4=9 \\ x=9-4 \\ x=5 \end{gathered}[/tex]Therefore, the solution of the system of equations is x=5 and y=16
