Chapter 7.1, Problem 28E

To determine

To find the solution of the system of linear equation.

Answer to Problem 28E

The value of x and y is $[1.88,3.25]$

Explanation of Solution

Given information:

The system of linear equation:

  $\begin{array}{l}-\frac{2}{3}x+y=2\mathrm{.....}\text{(}i\text{)}\\ 3x-\frac{1}{2}y=4\mathrm{.....}\text{(}ii\text{)}\end{array}$

Calculation :

To evaluate the values of variables x and y ,

It is needed to substitute the relation of two variables in the second equation obtained from first equation.

Therefore the relation of two variables in the first equation is obtained as:

  $\begin{array}{l}-\frac{2}{3}x+y=2\mathrm{.....}\text{(}i\text{)}\\ \text{y=2+}\frac{2x}{3}\mathrm{.....}\text{(}iii\text{)}\end{array}$

Now, substituting the value y in equation ( ii )

  $\begin{array}{l}3x-\frac{1}{2}\left(\frac{6+2x}{3}\right)=4\\ 3x-\frac{6-2x}{6}=4\\ \frac{18x-6-2x}{6}=4\\ 16x=30\\ x=30/16\\ x=1.88\end{array}$

Now, substituting the value of ‘x’ in equation ( ii ).

  $\begin{array}{l}3x-\frac{1}{2}y=4\\ 3(1.88)-0.5y=4\\ 5.64-4=0.5y\\ y=\frac{1.64}{0.5}\\ y=3.25\end{array}$

  

To check the solution of the two equation, use graphing utility to graph both the equation,

The graph is obtained as from the above graph, it can be observed that the point of intersection of the two line is $(x,y)=[1.88,3.25]$ so the solution is verified.

Hence, the solution of the two equation is $(x,y)=[1.88,3.25]$ .