Question

Solve each system by elimination:$\left\{\begin{array}{l}x+\frac{3}{5}y=-\frac{1}{5}\\ -\frac{1}{2}x-\frac{2}{3}y=\frac{5}{6}\end{array}\right.$

Short answer

The value of$x,y$are$1,-2$respectively

Step-by-step solution

Given information

Given the system of equations$\left\{\begin{array}{l}x+\frac{3}{5}y=-\frac{1}{5}\\ -\frac{1}{2}x-\frac{2}{3}y=\frac{5}{6}\end{array}\right.$

 Isolate the value of x

The value on isolating $x$is $x=-\frac{1}{5}-\frac{3}{5}y$. Substituting in other equation, we get

$\left[-\frac{1}{2}\left(-\frac{1}{5}-\frac{3}{5}y\right)-\frac{2}{3}y=\frac{5}{6}\right]$

$\left[\frac{3-11y}{30}=\frac{5}{6}\right]$

Solve for y

On solving, we get

$\left[\frac{3-11y}{30}=\frac{5}{6}\right]$

$y=-2$

Substituting value to calculate $x$, we get

$$\begin{gathered} x=-\frac{1}{5}-\frac{3}{5}(-2) \\ x=1 \end{gathered}$$

Checking the value

Substituting, we get

$$\begin{gathered} 1+\frac{3}{5}(-2)=-\frac{1}{5} \\ 1-\frac{6}{5}=\frac{-1}{5} \\ -\frac{1}{5}=\frac{-1}{5} \end{gathered}$$

Checking the value

Substituting, we get

$$\begin{gathered} -\frac{1}{2}\left(1\right)-\frac{2}{3}(-2)=\frac{5}{6} \\ -\frac{1}{2}+\frac{4}{3}=\frac{5}{6} \\ \frac{5}{6}=\frac{5}{6} \end{gathered}$$

So the value is correct