Chapter SH, Problem 8.10.4EP

To determine

To calculate: To solve the system of equations by graphing

Answer to Problem 8.10.4EP

Solutions of system of equations is $\left(4,5\right)$

Explanation of Solution

Given information:System of equations are $-x+2y=6$ and $x+4y=24$

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

  $\begin{array}{l}-x+2y=6\\ x+4y=24\end{array}$

Solving $-x+2y=6$

When $x=0$

  $\begin{array}{l}-0+2y=6\\ 2y=6\\ y=3\end{array}$

When $y=0$

  $\begin{array}{l}-x+2\left(0\right)=6\\ -x=6\\ x=-6\end{array}$

Solution of the equation are $\left(0,3\right),\left(-6,0\right)$

Solving $x+4y=24$

When $x=0$

  $\begin{array}{l}0+4y=24\\ 4y=24\\ y=6\end{array}$

When $y=0$

  $\begin{array}{l}x+4\left(0\right)=24\\ x+0=24\\ x=24\end{array}$

Solution of the equation are $\left(0,6\right),\left(24,0\right)$

Plotting the above points on graph,

From the graph, the lines intersect at point $\left(4,5\right)$

Thus, solution is $\left(4,5\right)$

Conclusion:

Hence, solutions of system of equations is $\left(4,5\right)$