Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 1–4, 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.
$\left\{\begin{array}{l}\frac{1}{3}x-2y=1\\ 5x-30y=18\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system of equations $\left\{\begin{array}{l}\frac{1}{3}x-2y=1\\ 5x-30y=18\end{array}\right.$ is $\left(\right(3+6a),a)$

Step 1. Given

The system of equations:

$\left\{\begin{array}{l}\frac{1}{3}x-2y=1\\ 5x-30y=18\end{array}\right.$

Step 2. Solve for x

Solve the first equation for x,

$$\begin{gathered} \frac{1}{3}x-2y=1 \\ \frac{1}{3}x=1+2y \\ x=3+6y \end{gathered}$$

Step 3. Solve for y

Substitute $x=3+6y$ in the second equation,

$$\begin{gathered} 5(3+6y)-30y=18 \\ 15+30y-30y=18 \end{gathered}$$

y will get cancelled, so take y as a constant and x  to be any other variable

Step 4. Find the solution

Take $y=a$ and

$x=3+6a$

Thus the solution set is $\left(\right(3+6a),a)$