Question

Find the solution to the following system of equations. x-2/3y=8 -1/5x+1/3y = 3

Answer 1

Note: Your question sounds a little unclear, but I am assuming that your system of equations is:

$x-\frac{2}{3}y=8$

$-\frac{1}{5}x+\frac{1}{3}y\:=\:3$

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:

$x=\frac{70}{3},\:y=23$

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}x-\frac{2}{3}y=8\\ -\frac{1}{5}x+\frac{1}{3}y=3\end{bmatrix}$

$\mathrm{Multiply\:}-\frac{1}{5}x+\frac{1}{3}y=3\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:-x+\frac{5}{3}y=15$

$\begin{bmatrix}x-\frac{2}{3}y=8\\ -x+\frac{5}{3}y=15\end{bmatrix}$

so adding the equation

$-x+\frac{5}{3}y=15$

$+$

$\underline{x-\frac{2}{3}y=8}$

$y=23$

so the system equations become

$\begin{bmatrix}x-\frac{2}{3}y=8\\ y=23\end{bmatrix}$

$\mathrm{For\:}x-\frac{2}{3}y=8\mathrm{\:plug\:in\:}y=23$

$x-\frac{2}{3}\cdot \:23=8$

$x-\frac{46}{3}=8$

Add 46/3 to both sides

$x-\frac{46}{3}+\frac{46}{3}=8+\frac{46}{3}$

$x=\frac{70}{3}$

Therefore, the solution of the system of equations be:

$x=\frac{70}{3},\:y=23$