Chapter 9.1, Problem 91SR

To determine

To Find:

The solution of system of linear equations using the elimination.

Answer to Problem 91SR

The solution is (4,2)

Explanation of Solution

Given Information:

System of linear equations :

  $\begin{array}{l}2x-3y=2\\ 5x+4y=28\end{array}$

Concept Used:

Elimination Method for solving the linear equation:

In this , we either add or subtract the linear equations to get the resulting equation in one variable by elimination the other variable.

When the coefficients are opposite in sign , you add the equations and when the coefficients of the equations are same in sign , you subtract the equations.

Calculation:

• Given

  $\begin{array}{l}2x-3y=\mathrm{2........................}(1)\\ 5x+4y=\mathrm{28......................}(2)\end{array}$

• Solving it :

Multiplying equation (1) by 4 and equation (2) by 3, the coefficients of the y-terms are additive inverses .

  $\begin{array}{l}2x-3y=\mathrm{2.........................}(1)\\ 5x+4y=\mathrm{28........................}(2)\\ Now,\\ 4(2x-3y=2)\mathrm{........................}[multiply"4"each\_side\_of\_(1)]\\ 3(5x+4y=28)\mathrm{......................}[multiply"3"each\_side\_of\_(2)]\\ \Rightarrow 8x-12y=\mathrm{8.................}(1)\\ \&15x+12y=\mathrm{84.....................}(2)\\ (1)+(2)\\ \Rightarrow 23x=92\\ \Rightarrow \frac{23x}{23}=\frac{92}{23}=\mathrm{4..................}[divide"23"each\_side]\\ \Rightarrow x=4\\ Substiuting\_x=4\_in(1)\\ \Rightarrow 8(4)-12y=\mathrm{8.................}[x=4]\\ \Rightarrow 32-12y=8\\ \Rightarrow 32-12y-32=8-\mathrm{32.........}[subtract"32"each\_side]\\ \Rightarrow -12y=-24\\ \Rightarrow \frac{-12y}{-12}=\frac{-24}{-12}=\mathrm{2.......................}[divide"-12"each\_side]\\ \Rightarrow y=2\end{array}$

So, the solution is (4,2)