Chapter 9.1, Problem 90SR

To determine

To Find:

The solution of system of linear equations using the elimination.

Answer to Problem 90SR

The solution is (6,4)

Explanation of Solution

Given Information:

System of linear equations :

  $\begin{array}{l}4x-3y=12\\ x+2y=14\end{array}$

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

  $\begin{array}{l}4x-3y=\mathrm{12......................}(1)\\ x+2y=\mathrm{14........................}(2)\end{array}$

• Solving it :

Multiplying equation (2) by -4, the coefficients of the x-terms are additive inverses .

  $\begin{array}{l}4x-3y=\mathrm{12.......................}(1)\\ x+2y=\mathrm{14........................}(2)\\ Now,\\ -4(x+2y=14)\mathrm{......................}[multiply"-4"each\_side\_of\_(2)]\\ \Rightarrow -4x-8y=-\mathrm{56.................}(2)\\ \&4x-3y=\mathrm{12.....................}(1)\\ (1)+(2)\\ \Rightarrow -11y=-44\\ \Rightarrow \frac{-11y}{-11}=\frac{-44}{-11}=\mathrm{4..................}[divide"-11"each\_side]\\ \Rightarrow y=4\\ Substiuting\_y=4\_in(1)\\ \Rightarrow 4x-3(4)=\mathrm{12.................}[y=4]\\ \Rightarrow 4x-12=12\\ \Rightarrow 4x-12+12=12+\mathrm{12.........}[add"12"each\_side]\\ \Rightarrow 4x=24\\ \Rightarrow \frac{4x}{4}=\frac{24}{4}=\mathrm{6.......................}[divide"4"each\_side]\\ \Rightarrow x=6\end{array}$

So, the solution is (6,4)