Q. 29 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The given system of equations has infinite number of solutions.

Step 1. Given information.

The given equations are:

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

Step 2. Determine one variable in terms of another variable.

The first equation can be written as:

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

Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

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

This statement is true for all real values. So, the given system of equations has infinite number of solutions.