Question

In the following exercises, solve the systems of equations by substitution.

$\left\{\begin{array}{l}y=-\frac{1}{3}x+2\\ x+3y=6\end{array}\right.$

Short answer

The system of linear equations has infinitely many solutions.

Step-by-step solution

Step 1. Given information.

The system of linear equations,

$\left\{\begin{array}{l}y=-\frac{1}{3}x+2\\ x+3y=6\end{array}\right.$

Step 2. Substituting the value of y from one equation into another equation.  

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

Now substituting this in another equation we get

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

Therefore the system of linear equations has infinitely many solutions.