Chapter 8.3, Problem 1DGP

To determine

To calculate:To find four solutions for the below equation and to write the solutions as ordered pair −

  $y=-4x-6$

Answer to Problem 1DGP

The four solutions as ordered pairs are $\left(-2,2\right)$ , $\left(-1,-2\right)$ , $\left(0,-6\right)$ and $\left(1,-10\right)$ .

Explanation of Solution

Given information:

Equation is $y=-4x-6$

Formula Used:

To solve an equation with multiple variables, we need to consider some random values for one of the variables and solve for the other one to find the ordered pair.

Calculation:

Given equation is $y=-4x-6$

Using the above explanation, we have -

Let the value of $x$ be $-2$ , substituting the value of $x$ in the above equation, we have:

  $y=-4\left(-2\right)-6$

Solving the above equation, we have :

  $\begin{array}{l}y=8-6\\ y=2\end{array}$

Thus, the first ordered pair is $\left(-2,2\right)$ .

Using the same approach to find the other ordered pairs −

Let the value of $x$ be $-1$ , substituting the value of $x$ in the above equation, we have:

  $y=-4\left(-1\right)-6$

Solving the above equation, we have :

  $\begin{array}{l}y=4-6\\ y=-2\end{array}$

Thus, the second ordered pair is $\left(-1,-2\right)$ .

Let the value of $x$ be $0$ , substituting the value of $x$ in the above equation, we have:

  $y=-4\left(0\right)-6$

Solving the above equation, we have :

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

Thus, the third ordered pair is $\left(0,-6\right)$ .

Let the value of $x$ be $1$ , substituting the value of $x$ in the above equation, we have:

  $y=-4\left(1\right)-6$

Solving the above equation, we have :

  $\begin{array}{l}y=-4-6\\ y=-10\end{array}$

Thus, the fourth ordered pair is $\left(1,-10\right)$ .

Thus, the four ordered pairs are $\left(-2,2\right)$ , $\left(-1,-2\right)$ , $\left(0,-6\right)$ and $\left(1,-10\right)$ .