Question

How do you find the ordered pair which is a solution of the equation \[2x - y = 9\]?

Answer 1

Hint: Here, we will substitute any value for \[x\] to find the possible values of \[y\]. The values of \[\left( {x,y} \right)\] will be the required ordered pair which is the solution of the given equation. But, in case, if there are infinite numbers of possible ordered pairs, then, we cannot determine a single solution for this equation.

Complete step-by-step answer:
According to the question,
In order to find an ordered pair that is a solution to an equation, we can perform a test.
In this test, we take the \[x\] value in the ordered pair and substitute it in the given equation. After simplifying the equation and solving for. If the \[y\] value is the same as the \[y\] value in the ordered pair, then, the ordered pair is a solution of the equation.
Now, for this question, the given equation is: \[2x - y = 9\]
Here, substituting \[x = 0\], we get,
\[2\left( 0 \right) - y = 9\]
\[ \Rightarrow y = - 9\]
Therefore, the ordered pair is \[\left( {0, - 9} \right)\]
Now, substituting \[x = 1\], we get,
\[2\left( 1 \right) - y = 9\]
\[ \Rightarrow y = 2 - 9 = - 7\]

Therefore, the ordered pair is \[\left( {1, - 7} \right)\]

Hence, as we can notice, there are infinite numbers of possible ordered pairs.
Hence, we cannot find a particular solution for the equation as this equation is having an infinite number of ordered pairs.
Thus, this is the required answer.

Note: An ordered pair is a composition of the \[x\] coordinate also known as the abscissa and the \[y\] coordinate which is called the ordinate. In an ordered pair, the two values are written in a fixed order. It helps to locate a point on the Cartesian plane for better visual comprehension. All the ordered pairs forming a line or lying on a line are the solution of the equation of that particular line. Whereas, those ordered pairs which do not lie on that line or which do not satisfy the equation of that line, then, are not the solution of that particular line.