Chapter SH, Problem 8.10.1EP

To determine

To calculate: To solve the system of equations by graphing

Answer to Problem 8.10.1EP

Solutions of system of equations is $\left(-3,1\right)$

Explanation of Solution

Given information:System of equations are $x+y=-2$ and $2x-3y=-9$

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

  $\begin{array}{l}x+y=-2\\ 2x-3y=-9\end{array}$

Solving $x+y=-2$

When $x=0$

  $\begin{array}{l}0+y=-2\\ y=-2\end{array}$

When $y=0$

  $\begin{array}{l}x+0=-2\\ x=-2\end{array}$

Solution of the equation are $\left(0,-2\right),\left(-2,0\right)$

Solving $2x-3y=-9$

When $x=0$

  $\begin{array}{l}2\left(0\right)-3y=-9\\ -3y=-9\\ y=3\end{array}$

When $y=0$

  $\begin{array}{l}2x-3\left(0\right)=-9\\ 2x=-9\\ x=-4.5\end{array}$

Solution of the equation are $\left(0,3\right),\left(-4.5,0\right)$

Plotting the above points on graph,

From the graph, the lines intersect at point $\left(-3,1\right)$

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

Conclusion:

Hence, solutions of system of equations is $\left(-3,1\right)$