Note: Your question sounds a little unclear, but I am assuming that your system of equations is:
[tex]x-\frac{2}{3}y=8[/tex]
[tex]-\frac{1}{5}x+\frac{1}{3}y\:=\:3[/tex]
It would anyways clear your concept because the procedure to find the solutions remains the same for any set of a system of equations.
Answer:
The solution of the system of equations be:
[tex]x=\frac{70}{3},\:y=23[/tex]
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}x-\frac{2}{3}y=8\\ -\frac{1}{5}x+\frac{1}{3}y=3\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-\frac{1}{5}x+\frac{1}{3}y=3\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:-x+\frac{5}{3}y=15[/tex]
[tex]\begin{bmatrix}x-\frac{2}{3}y=8\\ -x+\frac{5}{3}y=15\end{bmatrix}[/tex]
so adding the equation
[tex]-x+\frac{5}{3}y=15[/tex]
[tex]+[/tex]
[tex]\underline{x-\frac{2}{3}y=8}[/tex]
[tex]y=23[/tex]
so the system equations become
[tex]\begin{bmatrix}x-\frac{2}{3}y=8\\ y=23\end{bmatrix}[/tex]
[tex]\mathrm{For\:}x-\frac{2}{3}y=8\mathrm{\:plug\:in\:}y=23[/tex]
[tex]x-\frac{2}{3}\cdot \:23=8[/tex]
[tex]x-\frac{46}{3}=8[/tex]
Add 46/3 to both sides
[tex]x-\frac{46}{3}+\frac{46}{3}=8+\frac{46}{3}[/tex]
[tex]x=\frac{70}{3}[/tex]
Therefore, the solution of the system of equations be:
[tex]x=\frac{70}{3},\:y=23[/tex]
