Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 1–10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.   

$\left\{\begin{array}{l}2x+5y=10\\ 4x+10y=20\end{array}\right.$

Step-by-Step Solution

Answer

The system has infinitely many solutions.

Step 1. Given Information

We are given a system of equations $\left\{\begin{array}{l}2x+5y=10\\ 4x+10y=20\end{array}\right.$.

We need to solve the system of using the method of substitution or the method of elimination. 

Step 2. Eliminate the variables

Multiply both sides of the first equation $2x+5y=10$ by $2$.

$\begin{array}{rcl}2(2x+5y)& =& 2·10\\ 4x+10y& =& 20\end{array}$

Now subtract this equation from the second equation.

$\begin{array}{rcl}4x+10y-(4x+10y)& =& 20-20\\ 4x+10y-4x-10y& =& 0\\ 0& =& 0\end{array}$

So we get a true statement.

So the system of equations have infinitely many solutions.