Chapter 12, Problem 10CCSR

To determine

To find: the solution of the equation in the form of order pair and choose correct order pair form the options given below.

Answer to Problem 10CCSR

The option I is correct option.

Explanation of Solution

Given:

  $\begin{array}{l}2x+5y=-11.\\ 10x+3y=11.\end{array}$

The options are:

  

Concept used:

The elimination method:

Either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites add the equations to eliminate a variable and when the coefficients of one variable are equal or subtract the equation to eliminate a variable.

Calculation:

  $\begin{array}{l}2x+5y=-\mathrm{11..........}\left(i\right)\\ 10x+3y=\mathrm{11.............}\left(ii\right)\end{array}$

The solution of the two equation can be solved using addition or elimination or substitution method.

Multiplying the equation $\left(i\right)$ by $5$ and $\left(ii\right)$ by $1$ :

  $\begin{array}{l}10x+25y=-\mathrm{55..........}\left(iii\right)\\ 10x+3y=\mathrm{11.............}\left(iv\right)\end{array}$

Taking elimination method by eliminating $x$ :

  $\begin{array}{l}22y=-66.\\ \Rightarrow y=-\frac{66}{22}=-3.\\ 10x+3\left(-3\right)=11.\\ x=2.\end{array}$

Hence, option I is correct option.