Question

Solving a System of Equations

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example 6

$\left\{\begin{array}{l}x-y=3\\ x+3y=7\end{array}\right.$

Short answer

The ordered pair for the given system of linear equations is $(4,1)$ and it has a unique solution.

The graph is,

Step-by-step solution

Step 1. Given information

We are given the system of linear equations that is-

$\left\{\begin{array}{l}x-y=3\\ x+3y=7\end{array}\right.$

Step 2. Concept used

We will simplify the two equations which have two variables to one variable and get the required pair of $(x,y)$

And we will determine if the equations have infinite solutions or not.

Step 3. Calculation

Given a system of linear equations is

$\left\{\begin{array}{l}x-y=3\\ x+3y=7\end{array}\right.$

We will subtract the given equations which give
$\begin{array}{l}0z-4y=-4\\ y=1\end{array}$

We will substitute the value of y in any of the equations

Let us consider the second equation which is

$x+3y=7$

After substitution, we get

$\begin{array}{l}x+3\times 1=7\\ x=7-3\\ x=4\end{array}$

The graph looks like,