Q. 21 - Precalculus Enhanced with Graphing Utilities

Question

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\left\{\begin{array}{c}3x=24\\ x+2y=0\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the given system of equation is $x=8, y=-4; (8,-4)$.

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}3x& =& 24\\ x+2y& =& 0\end{array}$

Step 2. Determine the value of one variable.

The first equation can be written as:

$\begin{array}{rcl}3x& =& 24\\ x& =& \frac{24}{3}\\ x& =& 8\end{array}$

Step 3. Determine the value of another variable.

Substitute $x=8$ in the second equation.

$\begin{array}{rcl}8+2y& =& 0\\ 2y& =& -8\\ y& =& \frac{-8}{2}\\ y& =& -4\end{array}$

The solution of the given system of equation is $x=8, y=-4; (8,-4)$.