Chapter SH, Problem 8.3.11EP

To determine

To calculate: To find the four solution of equation and write the solution in ordered pair

Answer to Problem 8.3.11EP

Solutions of equation are $\left(0,-2\right),\left(1,-\frac{5}{2}\right),\left(2,-3\right),\left(3,-\frac{7}{2}\right)$

Explanation of Solution

Given information:Equation is $2x+3y=12$

Calculation:

Equation is given as

  $x+2y=-4$

Rewriting the equation as below

  $\begin{array}{l}2y=-4-x\\ y=-\frac{4}{2}-\frac{1}{2}x\\ y=-2-\frac{1}{2}x\end{array}$

When $x=0$

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

When $x=1$

  $\begin{array}{l}y=-2-\frac{1}{2}\left(1\right)\\ y=-2-\frac{1}{2}\\ y=\frac{-4-1}{2}\\ y=-\frac{5}{2}\end{array}$

When $x=2$

  $\begin{array}{l}y=-2-\frac{1}{2}\left(2\right)\\ y=-2-\frac{2}{2}\\ y=-2-1\\ y=-3\end{array}$

When $x=3$

  $\begin{array}{l}y=-2-\frac{1}{2}\left(3\right)\\ y=-2-\frac{3}{2}\\ y=\frac{-4-3}{2}\\ y=-\frac{7}{2}\end{array}$

Solution of the equation are $\left(0,-2\right),\left(1,-\frac{5}{2}\right),\left(2,-3\right),\left(3,-\frac{7}{2}\right)$

Conclusion:

Hence, solutions of equation are $\left(0,-2\right),\left(1,-\frac{5}{2}\right),\left(2,-3\right),\left(3,-\frac{7}{2}\right)$