Chapter 9.6, Problem 2MRE

To determine

To find: the solution of each system using addition and subtraction method.

Answer to Problem 2MRE

The value of $\text{a}$ is $\frac{\text{-3}}{\text{7}}$ and $\text{b}$ is $\frac{9}{7}$ .

Explanation of Solution

Given:

  $\text{5a+4b=3}$ .

  $\text{2a+3b=3}$ .

Concept used:

In the elimination method:

Either add or subtract equation to get an equation in one variable.

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

Calculation:

According to the given equation:

  $\text{5a+4b=3}$ ………. $\left(\text{i}\right)$

  $\text{2a+3b=3}$ …………… $\left(\text{ii}\right)$

Multiplying the first equation by $\text{3}$ :

  $\text{15a+12b=9}$ ……… $\left(\text{iii}\right)$

Multiplying the second equation by 4:

  $\text{8a+12b=12}$ …………… $\left(\text{iv}\right)$

Eliminating the equation $\left(\text{iii}\right)$ and $\left(\text{iv}\right)$ :

  $\text{7a=-3}$ .

  $\text{a=-}\frac{3}{7}$ .

Similarly, by putting value of $\text{a}$ in equation $\left(\text{ii}\right)$ .

  $\text{2}\left(-\frac{3}{7}\right)\text{+3b=3}$ .

  $\text{3b=3+}\frac{6}{7}$ .

  $\text{3b=}\frac{27}{7}$ .

  $\text{b=}\frac{9}{7}$

Hence, the value of $\text{a}$ is $\frac{\text{-3}}{\text{7}}$ and $\text{b}$ is $\frac{9}{7}$ .