Q. 27 - Precalculus Enhanced with Graphing Utilities

Question

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

$\left\{\begin{array}{c}2x-y=0\\ 4x+2y=12\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the given system of equation is $x=1.5, y=3, (1.5,3)$.

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}2x-y& =& 0\\ 4x+2y& =& 12\end{array}$

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

The first equation can be written as:

$\begin{array}{rcl}2x-y& =& 0\\ -y& =& -2x\\ y& =& 2x\end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl}4x+2\left(2x\right)& =& 12\\ 4x+4x& =& 12\\ 8x& =& 12\\ x& =& \frac{12}{8}\\ x& =& 1.5\end{array}$

Step 4. Determine the value of another variable.

Substitute $x=1.5$ in $y=2x$.

$$\begin{gathered} y=2(1.5) \\ y=3 \end{gathered}$$

The solution of the given system of equation is $x=1.5, y=3, (1.5,3)$.