Question

Solve the system of equation$\left\{\begin{array}{l}y=-2x-1\\ y=-\frac{1}{3}x+4\end{array}\right.$by substitution

Short answer

The solution is$\left(-3,5\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

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

$y=-\frac{1}{3}x+4\cdots \cdots \left(2\right)$

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

$\Rightarrow -2x-1=-\frac{1}{3}x+4$

Step 3. Solve for x

$\Rightarrow -2x+\frac{1}{3}x=4+1$

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

$\Rightarrow \frac{-5x}{3}=5$

$\Rightarrow x=\frac{15}{-5}$

$\Rightarrow x=-3$

Step 4. Substitute value of x from step 3 in equation 1

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

$\Rightarrow y=6-1$

$\Rightarrow y=5$

Step 5. Checking solution  

Now we have $x=-3$and$y=5$

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

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

$\Rightarrow 5=5$

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

$\Rightarrow 5=-\frac{1}{3}\left(-3\right)+4$

$\Rightarrow 5=5$