Chapter SH, Problem 8.10.3EP

To determine

To calculate: To solve the system of equations by graphing

Answer to Problem 8.10.3EP

Solutions of system of equations is $\left(5,2\right)$

Explanation of Solution

Given information:System of equations are $3x-2y=11$ and $-x+6y=7$

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

  $\begin{array}{l}3x-2y=11\\ -x+6y=7\end{array}$

Solving $3x-2y=11$

When $x=0$

  $\begin{array}{l}3\left(0\right)-2y=11\\ -2y=11\\ y=-5.5\end{array}$

When $y=0$

  $\begin{array}{l}3x-2\left(0\right)=11\\ 3x=11\\ y=\frac{11}{3}\end{array}$

Solution of the equation are $\left(0,-5.5\right),\left(\frac{11}{3},0\right)$

Solving $-x+6y=7$

When $x=0$

  $\begin{array}{l}-0+6y=7\\ 6y=7\\ y=\frac{7}{6}\end{array}$

When $y=0$

  $\begin{array}{l}-x+6\left(0\right)=7\\ x=-7\end{array}$

Solution of the equation are $\left(0,\frac{7}{6}\right),\left(-7,0\right)$

Plotting the above points on graph,

From the graph, the lines intersect at point $\left(5,2\right)$

Thus, solution is $\left(5,2\right)$

Conclusion:

Hence, solutions of system of equations is $\left(5,2\right)$