Chapter 3.2, Problem 29PPS

To determine

To find:the solution of the given system of equation using elimination.

Answer to Problem 29PPS

  $a=0;b=4$ .

Explanation of Solution

Given:

The given system of equation is $\begin{array}{l}2a-5b=-20\\ 2a+5b=20\end{array}$ .

Concept used:

Guidelines for solving system of equation using elimination:

1. First one of expression of the first equation is equivalent to the same expression of the second equation by multiplying.
2. Subtract both the equation.

Calculation:

Asthe given system of equation is $\begin{array}{l}2a-5b=-20\\ 2a+5b=20\end{array}$ .

Since one of the expressions is same on both the equation, therefore subtract the equation

  $\begin{array}{l}\underset{\_}{\begin{array}{l}2a-5b=-20\\ 2a+5b=20\\ ---\end{array}}\\ -10b=-40\\ \therefore b=\frac{-40}{-10}\\ \Rightarrow b=4\end{array}$

Now, substitutes the value of bin2^ndequation , then:

  $\begin{array}{l}2a+5b=20\\ 2a+5\left(4\right)=20\{\because b=4\}\\ 2a+20-20=20-20\{\text{subtract }20\text{on both the sides}}\\ \therefore 2a=0\\ \therefore a=0\end{array}$

Hence, the value ofgiven system of equation is $a=0;b=4$ .