Chapter 5.4, Problem 2Q

To determine

To calculate:

Solution of the linear equations using given graph.

Answer to Problem 2Q

There is no solution of the system

Explanation of Solution

Given information:

  $\begin{array}{l}y=\frac{1}{2}x-1\\ y=4x+6\end{array}$

Calculation:

Given graph is,

  

Given equations are,

  $\begin{array}{l}y=\frac{1}{2}x-\mathrm{1...}\left(i\right)\\ y=4x+\mathrm{6..}\left(ii\right)\end{array}$

Given equations are in slope intercept form,

Clearly slope of first line is $\frac{1}{2}$

And slope of the second line is $4$

Slopes are not equal.

Thus, both lines 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 $\left(-2,-2\right)$

Thus required solution is $\left(-2,-2\right)$

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

For checking the solution:

Put, $x=-2,y=-2$ in first equation,

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

For checking solutions,

Put $x=-2,y=-2$ in second equation,

  $\begin{array}{l}y=4x+6\\ -2=4\left(-2\right)+6\\ -2=8\end{array}$

Both equations are not satisfied

Hence the solution of the system is not available.