Chapter 8, Problem 1R

To determine

To calculate: The complete ordered pair solution of $\left(3,\right),\left(0,\right)\text{ and }\left(-4,\right)$ for the given equation $x+2y=8$.

Answer to Problem 1R

Solution:

The ordered pair of the equation $x+2y=8$ is $\left(3,\frac{5}{2}\right),\left(0,4\right)\text{ and }\left(-4,6\right)$.

Explanation of Solution

Given Information:

The equation is;

$x+2y=8$

And incomplete ordered pair is $\left(3,\right),\left(0,\right)\text{ and }\left(-4,\right)$.

Calculation:

Consider the equation,

$x+2y=8$

First of all we solve the equation for the y,

$x+2y=8$

Subtract $x$ from both sides as;

$\begin{array}{c}-x+x+2y=-x+8\\ 2y=-x+8\end{array}$

Divide by 2 on both the sides,

$\begin{array}{c}\frac{2y}{2}=\frac{-x}{2}+\frac{8}{2}\\ y=\frac{-x+8}{2}\end{array}$

Solve the equation with help of values of $x$ as;

Values of $x$	$y=\frac{-x+8}{2}$	Values of $y$	Ordered pair
3	$\begin{array}{c}y=\frac{-3+8}{2}\\ =\frac{5}{2}\end{array}$	$y=\frac{5}{2}$	$\left(3,\frac{-5}{2}\right)$
0	$\begin{array}{c}y=\frac{0+8}{2}\\ =4\end{array}$	$y=4$	$\left(0,4\right)$
$-4$	$\begin{array}{c}y=\frac{4+8}{2}\\ =6\end{array}$	$y=6$	$\left(-4,6\right)$

Hence, the ordered pair of the equation $x+2y=8$ is $\left(3,\frac{5}{2}\right),\left(0,4\right)\text{ and }\left(-4,6\right)$.