Question

How do you find five ordered pairs of $4x-y=8$?

Answer 1

Hint: Try to express the given equation in terms of ‘y’. Then take five different values of ‘x’ and put those values in the modified equation, to get the corresponding ‘y’ values. Write the corresponding ‘x’ and ‘y’ values in the order (x, y).

Complete step by step solution:
The given equation $4x-y=8$ can be expressed in terms of ‘y’ as
$\Rightarrow y=4x-8$
Ordered pair: An ordered pair is a composition of the ‘x’ coordinate (abscissa) and the ‘y’ coordinate (ordinate), having two values written in a fixed order within parentheses as (x, y).
To obtain five ordered pairs of the given equation, we have to take five different ‘x’ values and substitute into the above equation for corresponding values of ‘y’.
Let the values of ‘x’ are 2, 3, 4, 5 and 6
Putting x=2 in $y=4x-8$, we get
$\begin{align}
  & \Rightarrow y=4\times 2-8 \\
 & \Rightarrow y=8-8 \\
 & \Rightarrow y=0 \\
\end{align}$
So, the ordered pair is (2, 0)
Putting x=3 in $y=4x-8$, we get
$\begin{align}
  & \Rightarrow y=4\times 3-8 \\
 & \Rightarrow y=12-8 \\
 & \Rightarrow y=4 \\
\end{align}$
So, the ordered pair is (3, 4)
Putting x=4 in $y=4x-8$, we get
$\begin{align}
  & \Rightarrow y=4\times 4-8 \\
 & \Rightarrow y=16-8 \\
 & \Rightarrow y=8 \\
\end{align}$
So, the ordered pair is (4, 8)
Putting x=5 in $y=4x-8$, we get
$\begin{align}
  & \Rightarrow y=4\times 5-8 \\
 & \Rightarrow y=20-8 \\
 & \Rightarrow y=12 \\
\end{align}$
So, the ordered pair is (5, 12)
Putting x=6 in $y=4x-8$, we get
$\begin{align}
  & \Rightarrow y=4\times 6-8 \\
 & \Rightarrow y=24-8 \\
 & \Rightarrow y=16 \\
\end{align}$
So, the ordered pair is (6, 16)
These are the five required ordered pairs.

Note:
The application of ordered pairs in coordinate geometry is to represent geometric figures and objects in an open space. In Geometric shapes like circle, triangle, square, rectangle and polygons the ordered pairs are used to represent the center, vertices and the length of the sides with coordinates.