Chapter 5.3, Problem 23E

To determine

To calculate:

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

  $\begin{array}{l}3x+2y=4\\ 2y=8-5x\end{array}$

Answer to Problem 23E

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

Explanation of Solution

Given information:

  $\begin{array}{l}3x+2y=4\\ 2y=8-5x\end{array}$

Calculation:

The given equations are as:

  $3x+2y=4$................ (1)

  $2y=8-5x$

  $5x+2y=8$................ (2)

From above listed two equations, the coefficient of variable $y$ is same. So by eliminating this 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 $y$ :

  $\begin{array}{l}3x+2y-5x-2y=4-8\\ -2x=-4\\ x=2\end{array}$

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

  $\begin{array}{l}5x+2y=8\\ 5\left(2\right)+2y=8\\ 2y=-2\\ y=-1\end{array}$

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