Chapter 3.5, Problem 28WE

To determine

To calculate: Solve each system.

Answer to Problem 28WE

So, solution of the given equations is $x=\frac{35}{22}\text{ and }y=\frac{5}{11}$ .

Explanation of Solution

Given information: The two equations are,

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

The given system has two variables and two equations. So, the given system will have only one solution.

Calculation:

Solving the given equations by Substitution method,

  $\begin{array}{l}2\left(y-x\right)=5+2x\mathrm{...}\left(1\right)\\ 2\left(y+x\right)=5-2y\mathrm{...}\left(2\right)\\ \text{On Solving equation }\left(1\right)\\ 2y-2x=5+2x\\ x=\frac{5+2y}{4}\\ \text{Substituting value of }x\text{ in equation }\left(2\right),\\ 2\times \left(y+\left(\frac{5+2y}{4}\right)\right)=5-2y\\ 2\times \left(\frac{5y+5+2y}{4}\right)=5-2y\\ 7y+5=10-4y\\ y=\frac{5}{11}\end{array}$

  $\begin{array}{l}\text{Putting value of }y\text{ in equation }\left(1\right)\\ 2\left(\frac{5}{11}+x\right)=5-2\times \left(\frac{5}{11}\right)\\ \left(\frac{10}{11}+2x\right)=5-\frac{10}{11}\\ x=\frac{35}{22}\end{array}$

So, solution of the given equations is $x=\frac{35}{22}\text{ and }y=\frac{5}{11}$ .