Chapter 5.3, Problem 12E

To determine

To calculate:

The solution of the following equations by the elimination method and verify the solution:

  $\begin{array}{l}8x-5y=11\\ 4x-3y=5\end{array}$

Answer to Problem 12E

The solution of $\begin{array}{l}8x-5y=11\\ 4x-3y=5\end{array}$ by the elimination method is $x,y=2,1$ .

Explanation of Solution

Given information:

  $\begin{array}{l}8x-5y=11\\ 4x-3y=5\end{array}$

Calculation:

The two equations are given as:

  $8x-5y=11$................ (1)

  $4x-3y=5$................ (2)

  $\times 2$

  $2\left(4x-3y\right)=5\times 2$

  $8x-6y=10$................ (3)

Take subtraction of equation (1) and (3) to eliminate variable $x$ :

  $\begin{array}{l}8x-5y-8x+6y=11-10\\ y=1\end{array}$

Now calculate the value of variable $x$ by putting value of $y=1$ in eq. (2):

  $\begin{array}{l}8x-6y=10\\ 8x-6\left(1\right)=10\\ 8x=16\\ x=2\end{array}$

Hence, by solving two equations by elimination method get variable values as $x,y=2,1$ .

Check for solution:

  $x,y=2,1$

Use eq. (2) as:

  $\begin{array}{l}8x-6y=10\\ 8\left(2\right)-6\left(1\right)=10\\ 16-6=10\\ 10=10\end{array}$

Hence, verified.