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

$\left\{\begin{array}{l}3x+2y=0\\ -x-2y=8\end{array}\right.$

Short answer

The ordered pair for the given system of linear equations is $(4,-6)$ 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-

$\left\{\begin{array}{l}3x+2y=0\\ -x-2y=8\end{array}\right.$

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

$\left\{\begin{array}{l}3x+2y=0\\ -x-2y=8\end{array}\right.$

We will add the given equations which give-

$\begin{array}{l}2x+0y=8\\ x=\frac{8}{2}\\ x=4\end{array}$

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

$-x-2y=8$

Let us consider the first equation which is-

$\begin{array}{l}-\left(4\right)-2y=8\\ -2y=12\\ y=\frac{-12}{2}\\ y=-6\end{array}$

The graph looks like,