Chapter SH, Problem 8.10.2EP

To determine

To calculate: To solve the system of equations by graphing

Answer to Problem 8.10.2EP

Solutions of system of equations is $\left(2,3\right)$

Explanation of Solution

Given information:System of equations are $y=2x-1$ and $y=x+1$

Formula Used:

The point of intersection of two lines is the solution of the system of linear equations

Calculation:

System of equation is given as

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

Solving $y=2x-1$

When $x=0$

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

When $y=0$

  $\begin{array}{l}0=2x-1\\ 2x=1\\ x=\frac{1}{2}\\ x=0.5\end{array}$

Solution of the equation are $\left(0,-1\right),\left(0.5,0\right)$

Solving $y=x+1$

When $x=0$

  $\begin{array}{l}y=0+1\\ y=1\end{array}$

When $y=0$

  $\begin{array}{l}0=x+1\\ x=-1\end{array}$

Solution of the equation are $\left(0,1\right),\left(-1,0\right)$

Plotting the above points on graph,

From the graph, the lines intersect at point $\left(2,3\right)$

Thus, solution is $\left(2,3\right)$

Conclusion:

Hence, solutions of system of equations is $\left(2,3\right)$