Chapter 11, Problem 4RE

To determine

To find: The solution of equation $\left\{\begin{array}{l}y=2x-5\\ x=3y+4\end{array}\right\}$ .

Answer to Problem 4RE

The solution of the equation is $\left(\frac{11}{5},-\frac{3}{5}\right)$ .

Explanation of Solution

Given information:

The given equation is $\left\{\begin{array}{l}y=2x-5\\ x=3y+4\end{array}\right\}$

Calculation:

Calculate the expression,

Substitute $x=3y+4$ in the equation $y=2x-5$ and simplify.

  $\begin{array}{l}y=2\left(3y+4\right)-5\\ y=6y+3\end{array}$

Add $-6y$ on both sides of the equation,

  $\begin{array}{c}y-6y=-6y+3-6y\\ -5y=3\end{array}$

Divide both sides of the equation by -5

  $\begin{array}{c}\frac{-5y}{5}=\frac{3}{-5}\\ y=-\frac{3}{5}\end{array}$

Back- substitute $-\frac{3}{5}$ for $y$ in the equation $x+3y+4$ ,

  $\begin{array}{l}x=3\left(-\frac{3}{5}\right)+4\\ x=\frac{11}{5}\end{array}$

Therefore, the solution expressed in ordered form is $\left(\frac{11}{5},-\frac{3}{5}\right)$

Check the solution ,

Check: $\begin{array}{l}\left\{\begin{array}{l}y=2x-5\\ x=3y+4\end{array}\right\}\\ -\frac{3}{5}=2\times \frac{11}{5}-5=-\frac{3}{5}\\ \frac{11}{5}=3\left(\frac{-3}{5}\right)+4=\frac{11}{5}\end{array}$

Therefore, the solution of the equation is $\left(\frac{11}{5},-\frac{3}{5}\right)$ .