Question

Solve the system of equation$\left\{\begin{array}{l}2x+5y=1\\ y=\frac{1}{3}x-2\end{array}\right.$by substitution

Short answer

The solution is$\left(3,-1\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$2x+5y=1\cdots \cdots \left(1\right)$

$y=\frac{1}{3}x-2\cdots \cdots \left(2\right)$

Step 2. Substitute value of y from equation 2  in equation 1

$\Rightarrow 2x+5\left(\frac{1}{3}x-2\right)=1$

Step 3. Solve for x

$\Rightarrow 2x+\frac{5}{3}x-10=1$

$\Rightarrow \frac{6x+5x}{3}=1+10$

$\Rightarrow \frac{11}{3}x=11$

$\Rightarrow x=\frac{33}{11}$

$\Rightarrow x=3$

Step 4. Substitute value of x from step 3 in equation 2

$\Rightarrow y=\frac{1}{3}\left(3\right)-2$

$\Rightarrow y=1-2$

$\Rightarrow y=-1$

Step 5. Checking solution 

Now we have $x=3$and $y=-1$

Put these values in equation $\left(1\right)$

$\Rightarrow 2\left(3\right)+5\left(-1\right)=1$

$\Rightarrow 1=1$

Also put these values in equation $\left(2\right)$

$\Rightarrow -1=\frac{1}{3}\left(3\right)-2$

$\Rightarrow -1=-1$