Chapter 5.4, Problem 1Q

To determine

To calculate:

Solution of the linear equations using given graph.

Answer to Problem 1Q

Solution of the system of equation is $\left(3,1\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}y=-\frac{1}{3}x+2\\ y=x-2\end{array}$

Calculation:

Given graph is,

  

Given equations are,

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

Given equations are in slope intercept form,

Clearly slope of first line is $-1$

And slope of the second line is $1$

Slopes are negative reciprocals of each other.

Thus, both lines are perpendicular so intersect each other.

To find the point of intersection, both lines on similar coordinate system is as below:

  

So from the above graph ,both lines are intersect at $\left(3,1\right)$

Thus required solution is $\left(3,1\right)$

Check the solution by substituting the coordinates of the point in each original equation.

For checking the solution:

Put, $x=3,y=1$ in first equation,

  $\begin{array}{l}y=-\frac{1}{3}x+2\\ 1=-\frac{1}{3}3+2\\ 1=-\frac{1}{3}3+2\\ 1=1\end{array}$

For checking solutions,

Put $x=3,y=1$ in second equation,

  $\begin{array}{l}y=x-2\\ 1=3-2\\ 1=1\end{array}$

Both equations are satisfied

Hence the solution of the system of equation is $\left(3,1\right)$