Q. 22 - Precalculus Enhanced with Graphing Utilities

Question

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

$\left\{\begin{array}{c}4x+5y=-3\\ -2y=-8\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the given system of equation is $x=-5.75, y=4; (-5.75,4)$.

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}4x+5y& =& -3\\ -2y& =& -8\end{array}$

Step 2. Determine the value of one variable.

The second equation can be written as:

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

Step 3. Determine the value of another variable.

Substitute $y=4$ in the first equation.

$\begin{array}{rcl}4x+5\left(4\right)& =& -3\\ 4x+20& =& -3\\ 4x& =& -3-20\\ x& =& \frac{-23}{4}\\ x& =& -5.75\end{array}$

The solution of the given system of equation is $x=-5.75, y=4; (-5.75,4)$.