Question

How do you find three different ordered pairs $y = 2x + 1$ ?

Answer 1

We are given a linear equation and we have to find the values of $x$ and $y$ that will satisfy the equation. Then write the values of $x$ and $y$ in the form of an ordered pair $\left( {x,y} \right)$. We will find such values by substituting different values of $x$ into the equation. Then we will solve the equation and find the value of the remaining one variable.

Complete step-by-step answer:
Step 1: We are given a linear equation $y = 2x + 1$ by applying the method of substitution we will find the value of $y$. First we will substitute $x = 0$ into the equation.
$\Rightarrow y = 2\left( 0 \right) + 1$
On proper rearrangement we will get:
$\Rightarrow y = 0 + 1$
$\Rightarrow y = 1$
Now, we will write the values of $x$ and $y$ in the form of ordered pair $\left( {0,1} \right)$
Step2: Now we will substitute the value of $x = - 1$ in the equation and solve for $y$:
$\Rightarrow y = 2\left( { - 1} \right) + 1$
On proper rearrangement we will get:
$\Rightarrow y = - 2 + 1$
$\Rightarrow y = - 1$
Now, we will write the values of $x$ and $y$ in the form of second ordered pair $\left( { - 1, - 1} \right)$
Step3: Now we will substitute the value of $x = 1$ in the equation and solve for $y$:
$\Rightarrow y = 2\left( 1 \right) + 1$
On proper rearrangement we will get:
$\Rightarrow y = 2 + 1$
$\Rightarrow y = 3$
Now, we will write the values of $x$ and $y$ in the form of second ordered pair $\left( {1,3} \right)$

Hence the three different ordered pairs are $\left( {0,1} \right)$, $\left( { - 1, - 1} \right)$ and $\left( {1,3} \right)$.

Note:
Such types of questions mainly don't get an approach on how to solve it. In these types of questions, the value of one variable can find out by substituting different values of another variable. Many times there are chances of getting errors while solving the equation by substituting some value of a variable.