Chapter SH, Problem 3.4EP

To determine

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

Answer to Problem 3.4EP

  $a=-1;b=-2$ .

Explanation of Solution

Given:

The given system of equation is $\begin{array}{l}-5a+2b=16\\ 4a-5b=-6\end{array}$ .

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 or add both the equation.

Calculation:

As the given system of equation is $\begin{array}{l}-5a+2b=16\\ 4a-5b=-6\end{array}$ .

Since none of the expressions is same on both the equation, therefore multiply eq(1) by 4 andeq(2) by 5 andthen add the equation:

  $\begin{array}{l}4\left(-5a+2b\right)=16\times 4\\ -20a+8b=64\\ 5\left(4a-5b\right)=-6\times 5\\ 20a-25b=-30\end{array}$

  $\begin{array}{l}\underset{\_}{\begin{array}{l}-20a+8b=64\\ 20a-25b=-30\\ +-+\end{array}}\\ -17b=34\\ \therefore b=\frac{34}{-17}\\ \Rightarrow b=-2\end{array}$

Now, substitutes the value of bin 1st equation, then:

  $\begin{array}{l}4a-5b=6\\ 4a-5\left(-2\right)=6\{\because b=-2\}\\ 4a+10=6\{\text{multiply}}\\ \therefore 4a=-4\{\text{subtract}4\text{on both the sides}}\\ \Rightarrow a=\frac{-4}{4}\\ a=-1\end{array}$

Hence, the value of given system of equation is $a=-1;b=-2$ .