Exercise 37 Page 355

We are given that the solution of a system of linear equations is $(\text{-}3,2).$ We are also given one of the equations of the system. We need to find a second equation for this system. Please be note that there are infinitely many possible answers to this exercise. Here we will examine only one possible solution.

Finding the Equation

We can write any equation in which $(\text{-}3,2)$ is the answer. We know that $\text{-}3$ is the solution for the $x\text{-}$variable and $2$ the solution for the $y\text{-}$variable. Let's write an equation by adding these values.

Checking the Answer

We can write a system of equations using the given equation and the one we created. To check that the equation we created works, let's solve the system. Since the coefficient of the $x\text{-}$variable is $1$ in both equations, we will use the Elimination Method. To do so we will subtract Equation (II) from Equation (I). We have found that $y=2.$ To find $x,$ we will substitute $2$ for $y$ in Equation (II). We have that $x=\text{-}3.$ With the obtained values, we can see that the solution of the system is $(\text{-}3,2).$ This matches the solution given in the exercise. Therefore, the equation we wrote is correct.