Q. 20 - Precalculus Enhanced with Graphing Utilities

Question

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\left\{\begin{array}{c}x+3y=5\\ 2x-3y=-8\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the given system of equation is $x=-1, y=2; (-1,2)$.

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}x+3y& =& 5\\ 2x-3y& =& -8\end{array}$

Step 2. Determine the value of one variable by substitution.

The first equation can be written as:

$x=5-3y$

Substitute this in the second equation.

$\begin{array}{rcl}2(5-3y)-3y& =& -8\\ 10-6y-3y& =& -8\\ -9y& =& -8-10\\ y& =& \frac{-18}{-9}\\ y& =& 2\end{array}$

Step 3. Determine the value of another variable.

Substitute $y=2$ in $x=5-3y$.

$\begin{array}{rcl}x& =& 5-3\left(2\right)\\ & =& 5-6\\ & =& -1\end{array}$

The solution of the given system of equation is $x=-1, y=2; (-1,2)$.