Chapter 5.3, Problem 2E

To determine

To Explain:How to solve the given system of linear equations by elimination.

Answer to Problem 2E

The required solution is $x=-5,y=-2$

Explanation of Solution

Given information:

  $\begin{array}{l}\\ 2x-3y=-4\text{ Equation 1}\\ -5x+9y=7\text{ Equation 2}\end{array}$

Calculation:

Multiply Equation 1 by 3 so that the co-efficient of y-terms are opposites

  $\begin{array}{l}\text{3}\left(2x-3y\right)=3\cdot \left(-4\right)\\ 6x-9y=-12\text{ Revised Equation 1}\end{array}$

Variable y can be eliminated by adding revised equation (i) and (ii)

  $\begin{array}{l}6x-9y=-12\\ \underset{\_}{-5x+9y=7}\\ x=-5\end{array}$

Now substitute the value of x in equation 1

  $\begin{array}{l}\Rightarrow 2\cdot \left(-5\right)-3y=-4\\ \Rightarrow -10-3y=-4\end{array}$

Add 10 on both sides

  $\begin{array}{l}\Rightarrow -10+10-3y=-4+10\\ \Rightarrow -3y=6\end{array}$

Divide -3 on both sides

  $\begin{array}{l}\Rightarrow \frac{-3y}{-3}=\frac{6}{-3}\\ \Rightarrow y=-2\end{array}$