Q. 32 - Precalculus Enhanced with Graphing Utilities

Question

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

$\left\{\begin{array}{c}3x-2y=0\\ 5x+10y=4\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the given system of equation is $x=0.2, y=0.3; \left(0.2,0.3\right)$.

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}3x-2y& =& 0\\ 5x+10y& =& 4\end{array}$

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

The first equation can be written as:

$\begin{array}{rcl}3x-2y& =& 0\\ 3x& =& 2y\\ x& =& \frac{2}{3}y\end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl}5\left(\frac{2}{3}y\right)+10y& =& 4\\ \frac{10y}{3}+10y& =& 4\\ \frac{10y+30y}{3}& =& 4\\ 40y& =& 12\\ y& =& \frac{12}{40}\\ y& =& 0.3\end{array}$

Step 4. Determine the value of another variable.

Substitute $y=0.3$ in $x=\frac{2}{3}y$.

$$\begin{gathered} x=\frac{2}{3}(0.3) \\ x=2(0.1) \\ x=0.2 \end{gathered}$$

The solution of the given system of equation is $x=0.2, y=0.3; \left(0.2,0.3\right)$.