Q. 341 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

The system of linear equations has infinitely many solutions. 

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.