Chapter 5.3, Problem 16E

To determine

To calculate:

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

  $\begin{array}{l}-2x-5y=9\\ 3x+11y=4\end{array}$

Answer to Problem 16E

The solution of $\begin{array}{l}-2x-5y=9\\ 3x+11y=4\end{array}$ by the elimination method is $x,y=-17,5$ .

Explanation of Solution

Given information:

  $\begin{array}{l}-2x-5y=9\\ 3x+11y=4\end{array}$

Calculation:

The two equations are given as:

  $-2x-5y=9$................ (1) $\times 3$

  $3\left(-2x-5y\right)=3\times 9$

  $-6x-15y=27$................ (2)

  $3x+11y=4$................ (3) $\times 2$

  $2\left(3x+11y\right)=2\times 4$

  $6x+22y=8$................ (4)

Take addition of equation (2) and (4) to eliminate variable $x$ :

  $\begin{array}{l}-6x-15y+6x+22y=27+8\\ 7y=35\\ y=5\end{array}$

Now calculate the value of variable $x$ by putting value of $y=5$ in eq. (2):

  $\begin{array}{l}-6x-15y=27\\ -6x-15\left(5\right)=27\\ -6x-75=27\\ -6x=102\\ x=-17\end{array}$

Hence, by solving two equations by elimination method get variable values as $x,y=-17,5$ .

Check for solution:

  $x,y=-17,5$

Use eq. (2) as:

  $\begin{array}{l}-6x-15y=27\\ -6\left(-17\right)-15\left(5\right)=27\\ 102-75=27\\ 27=27\end{array}$

Hence, verified.