Chapter 11, Problem 2CT

To determine

To find: The solution of equation $\left\{\begin{array}{l}\frac{1}{3}x-2y=1\\ 5x-30y=18\end{array}\right\}$ .

Answer to Problem 2CT

The solution of the equations is $\left(\frac{6}{5},\frac{-4}{5}\right)$ .

Explanation of Solution

Given information:

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

Calculation:

Calculate the equation,

  $\begin{array}{l}\frac{1}{3}x-2y=1\\ x=3\left(1+2y\right)\mathrm{......}\left(1\right)\end{array}$

Now we can substitute the above obtain relation in the first equation to obtain the possible values of $y$

  $\begin{array}{c}5\left(2\left(1+2y\right)\right)-30y=18\\ 10+20y-30y=18\\ y=-\frac{4}{5}\end{array}$

The obtain value of $y$ can be substitute in the equation (1) to obtain the value of $x$

  $\begin{array}{c}x=3\left(1+2\left(-\frac{4}{5}\right)\right)\\ x=\frac{6}{5}\end{array}$

Therefore, the solution of the equation is $\left(\frac{6}{5},\frac{-4}{5}\right)$ .