Question

How do you know if an ordered pair $(5,11)$ is a solution to $y = 2x + 1$ ?

Answer 1

Hint: If you are given an ordered pair solution to an equation, knowing whether it is a solution or not. We just have to substitute the given ordered pair into the equation and then evaluate whether it satisfies the given equation or not.

Complete step by step solution:
We have given an ordered pair that is $(5,11)$ , we have to check whether this ordered pair is the solution to $y = 2x + 1$ .
For this we have to substitute the given ordered pair into the equation and then evaluate whether it satisfies the given equation or not.
We have our equation as,
$y = 2x + 1$
Now substitute $x$equals to $5$ and $y$equals to $11$ ,
$ \Rightarrow 11 = 2(5) + 1$
$ \Rightarrow 11 = 11$
Here the right-hand side is equal to the left-hand side of the equation.
Therefore, we can say that this is a valid ordered pair .

Note: Functions are usually represented by a function rule where you express the variable, $y$ , in terms of the variable, $x$ . Here $y$ is dependent on $x$ . A pair of an input value and its corresponding output value is named an ordered pair and may be written as $(a,b)$. In an ordered pair the primary number, the input $a$, corresponds to the horizontal axis and also the second number, the output $b$, corresponds to the vertical axis.
A pairing of any set of inputs with their corresponding outputs is termed a relation. Every function may be a relation, but not all relations are functions.