Question

Solve the system of equations by substitution

$\left\{\begin{array}{l}y=-2x-1\\ y=-\frac{1}{3}x+4\end{array}\right.$

Short answer

The solution for the system of equations is,

$$\begin{gathered} x=-3 \\ y=5 \end{gathered}$$

Step-by-step solution

Step 1. Given the information

The system of equations is,

$\left\{\begin{array}{l}y=-2x-1\\ y=-\frac{1}{3}x+4\end{array}\right.$

Step 2. Substituting the value of y in the equation

Substituting $y=-2x-1$in the equation

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

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

role="math" localid="1644347591540" $-2x+\frac{1}{3}x=4+1$

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

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

$x=5÷\frac{-5}{3}$

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

$x=-3$

Step 3. Substituting the value of x in the equation.

Substituting $x=-3$in the equation

$y=-2x-1$

$y=-2(-3)-1$

$y=6-1$

$y=5$

Step 4. Checking the solution for the equation y=-2x-1

Substituting $$\begin{gathered} x=-3 \\ y=5 \end{gathered}$$in the equation

$y=-2x-1$

$5=-2(-3)-1$

$5=6-1$

$5=5$

This is true.

Step 5. Checking the solution for the equation y=-13x+4

Substituting $$\begin{gathered} x=-3 \\ y=5 \end{gathered}$$in the equation

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

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

$5=1+4$

$5=5$

This is true.