Q. 19 - Precalculus Enhanced with Graphing Utilities

Question

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{c}5x-y=21\\ 2x+3y=-12\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the given system of equation is $x=3, y=-6; (3,-6)$.

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}5x-y& =& 21\\ 2x+3y& =& -12\end{array}$

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

The first equation can be written as:

$\begin{array}{rcl}-y& =& 21-5x\\ y& =& 5x-21\end{array}$

Substitute this in the second equation.

$\begin{array}{rcl}2x+3(5x-21)& =& -12\\ 2x+15x-63& =& -12\\ 17x& =& -12+63\\ x& =& \frac{51}{17}\\ x& =& 3\end{array}$

Step 3. Determine the value of another variable.

Substitute $x=3$ in $y=5x-21$.

$\begin{array}{rcl}y& =& 5\left(3\right)-21\\ & =& 15-21\\ & =& -6\end{array}$

The solution of the given system of equation is $x=3, y=-6; (3,-6)$.