Chapter 5.4, Problem 3Q

To determine

To calculate:

Solution of the linear equations using given graph.

Answer to Problem 3Q

There is no solution of the system.

Explanation of Solution

Given information:

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

Calculation:

Given graph is,

  

Given equations are,

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

Given equations are in slope intercept form $y=mx+c$ ,

Clearly slope of first line is $0$

And slope of the second line is $2$

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 $\left(0,2\right)$

Thus required solution is $\left(0,2\right)$

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

For checking the solution:

Put, $x=0,y=2$ in first equation,

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

For checking solutions,

Put $x=0,y=2$ in second equation,

  $\begin{array}{l}y=2x+1\\ 2=2\left(0\right)+1\\ 2=1\end{array}$

Both equations are not satisfied

Hence the solution of the system is not available.