Chapter 8.3, Problem 37HP

To determine

To calculate: To write a linear equation that has $\left(3,-2\right)$ as a solution and then find another solution of the equation

Answer to Problem 37HP

Equation is $2x+3y=0$ and other solution is $\left(6,-4\right)$

Explanation of Solution

Given information: Solution of equation is $\left(3,-2\right)$

Calculation:

Given the solution of equation as

  $\left(3,-2\right)$

Since this is the solution, thus the equation of line must pass through the above points.

Let another point be $\left(0,0\right)$

Thus, equation of line is

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

Equation is given as

  $2x+3y=0$

Finding the solutions of the above equation:

When $x=6$

  $\begin{array}{l}12+3y=0\\ 3y=-12\\ y=-4\end{array}$

Thus, solution is $\left(6,-4\right)$

Conclusion:

Hence, Equation is $2x+3y=0$ and other solution is $\left(6,-4\right)$