Question

How do you find the ordered pair that satisfies $y=2x+5;\left( 2, ? \right)$ ?

Answer 1

Hint: We are given an equation as $y=2x+5$ we have to find the pair of $\left( 2, ? \right)$ such that it will satisfy the given equation. To find such, first learn the type of equation, and then find such. We first learn the type of equation, then we will see degree as we can see that we have to find ‘y’ so degree will tell us the number of ‘y’ possible, we will do some example of finding the ordered pair, once we get a grip we will start working on our problem.

Complete step by step solution:
We are given $y=2x+5$ , we can see that it has two variable ‘x’ and ‘y’ each one has degree 1, so clearly it is a linear equation in one variable, so it mean for each ‘x’, there is just as 1 ‘y’ possible since degree is given to us as 1. Now to find the ordered pair that satisfies any equation it means we have to find those values of ‘x’ and ‘y’ when we put them simultaneously in the equation they must satisfies the equation.
For example: Say we have $x+y=2$ if we consider $\left( 1,1 \right)$ so here $x=1$ , and $y=1$ because in ordered pair first term is ‘x’ and 2nd is ‘y’.
We put $x=1$ and $y=1$ is $x+y=2$ , we will get –
$1+1=2$ that is $2=2$ .
It satisfies the equation.
If we have just one coordinate given from the ordered pair that satisfies the equation, then we use that given coordinate into the equation and find the value of ‘y’, by solving the equation.
Say we have equation $x+2y=5$ , we are given $\left( 3, \right)$ satisfies, so we have $x=3$ , we put $x=3$ , in $x+2y=5$ , we get –
$3+2y=5$
Subtracting 3 on both side, we get –
$2y=5-3=2$
So $2y=2$
Dividing both sides by ‘2’, we get –
$\dfrac{2y}{2}=\dfrac{x}{2}$
So, $y=1$
Now, we work on our problem.
We have an equation as $y=2x+5$ and $\left( 2, \right)$ satisfies.
So, we put $x=2$ in $y=2x+5$ and solve for ‘y’.
So,
 $\begin{align}
  & y=2\left( 2 \right)+5 \\
 & =4+5 \\
 & y=9 \\
\end{align}$
So, we get ‘y’ as ‘9’.
Hence, the ordered pair is $\left( 2,9 \right)$ .

Note: We can cross check the solution by putting $x=2$ and $y=9$ in the given equation.
We cross check we put $x=2$ and $y=9$ in $y=2x+5$ . We get –
$9=2\left( 2 \right)+5$
By simplifying, we get –
$\begin{align}
  & 9=4+5 \\
 & 9=9 \\
\end{align}$
Which is true.
So, the solution achieved earlier is correct. Also number that $2x+5\ne 7x$ , we cannot add constant and variable together.