Q. 25

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

$\{\begin{matrix} 2 x + y = 1 \\ 4 x + 2 y = 3 \end{matrix}$

Verified

Answer

The given system of equations is inconsistent.

1Step 1. Given information.

The given equations are:

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

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

The first equation can be written as:

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

3Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

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

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