Chapter 8, Problem 20SGR

To determine

To find: four solutions and write as ordered pairs.

Answer to Problem 20SGR

The four ordered pair solution of the equation $x+y=-1$ is: $\left(-1,0\right),\left(0,-1\right),\left(1,-2\right),\left(2,-3\right)$

Explanation of Solution

Given:

Consider the equation: $x+y=-1$

Calculation:

First step is to separate the variable y

So, subtract both sides of equation by x

  $\begin{array}{l}x+y-x=-x-1\\ y=-x-1\end{array}$

Take different value of x and solve for y

Put $x=-1$ inequation.

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

Now, put $x=0$ in equation.

  $\begin{array}{c}y=-0-1\\ =-1\end{array}$

Put, $x=1$ in equation.

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

Put $x=2$ in equation.

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

Therefore, the complete table that shows different value of x and y is as follow:

x	y
$-1$	$0$
$0$	$-1$
$1$	$-2$
$2$	$-3$

Conclusion:

Therefore, the four ordered pair solution of the equation $x+y=-1$ is: $\left(-1,0\right),\left(0,-1\right),\left(1,-2\right),\left(2,-3\right)$