Chapter 5.3, Problem 25E

To determine

To calculate:

The solution of the following linear equations by using any correct method:

  $\begin{array}{l}y-x=2\\ y=-\frac{1}{4}x+7\end{array}$

Answer to Problem 25E

The solution of the $\begin{array}{l}y-x=2\\ y=-\frac{1}{4}x+7\end{array}$ by elimination method is $x,y=4,6$ .

Explanation of Solution

Given information:

  $\begin{array}{l}y-x=2\\ y=-\frac{1}{4}x+7\end{array}$

Calculation:

The given equations are as:

  $y-x=2$

  $-x+y=2$................ (1)

  $y=-\frac{1}{4}x+7$

  $\frac{1}{4}x+y=7$................ (2)

From above listed two equations, the coefficient of variable $y$ is same. So by eliminating variable $y$ , the value of $x$ is obtainable. So, the correct method to get the solutions is elimination method.

Take subtraction of equation (1) and (2) to eliminate variable $x$ :

  $\begin{array}{l}-x+y-\frac{1}{4}x-y=2-7\\ -\frac{5}{4}x=-5\\ x=4\end{array}$

Now calculate the value of variable $y$ by putting value of $x=4$ in eq. (1):

  $\begin{array}{l}-x+y=2\\ -4+y=2\\ y=6\end{array}$

Hence, by solving two equations by elimination method get variable values as $x,y=4,6$ .