Question

How do you determine which ordered pair is a solution of $y = 4x + 2$?

Answer 1

Hint: We will first see which ordered pair suitable for the given linear equation. We get the ordered pairs by substituting the value for any one of the variables $x$ and $y$.

Complete step-by-step solution:
We are given that we need to determine the suitable ordered pairs for the given equation $y = 4x + 2$.
First of all we take the values for any one of the variable $x$ and $y$,
If we put $x = 0$ in the given equation $y = 4x + 2$ then we will get,
$ \Rightarrow y = 4(0) + 2 = 2$
So when $x = 0$ we get $y = 2$, so the ordered pair is $\left( {0,2} \right)$
Now we put $x = 1$ in the given equation $y = 4x + 2$ then we will get,
$ \Rightarrow y = 4(1) + 2 = 6$
So when $x = 1$ we get $y = 6$, so the ordered pair is $\left( {1,6} \right)$ .
Here we see that if we need the ordered pair to be the solution of the given equation $y = 4x + 2$, then the variable $x$ and $y$ both together must satisfy the given equation.
Hence, when we need to determine whether some ordered pair satisfies the given equation or not, we just need to put the values of variable $x$ and $y$ to see whether they are giving an accurate answer or not.

Therefore ordered pair (0,2) and (1,6) satisfy the given equation.

Note: If you are given that you need to check whether $\left( {a,b} \right)$ is a solution of the given equation $y = 4x + 2$ then we just need to put $x = a$ and $y = b$.
For example if we want to see $\left( {4,3} \right)$ is a solution of the equation $y = 4x + 2$ we will put $x = 4$ and $y = 3$ we get right side of the equation $4(4) + 2 = 18$ and we get left hand side of the equation is $3$.