Question

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

$\left\{\begin{array}{c}2x+y=1\\ 4x+2y=3\end{array}\right.$

Short answer

The given system of equations is inconsistent.

Step-by-step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}2x+y& =& 1\\ 4x+2y& =& 3\end{array}$

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

The first equation can be written as:

$\begin{array}{rcl}2x+y& =& 1\\ y& =& 1-2x\end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl}4x+2(1-2x)& =& 3\\ 4x+2-4x& =& 3\\ 2& =& 3\end{array}$

This statement is false, it means the system has no solution. So, the given system of equations is inconsistent.