Question

How do you solve x in $y=5x+9$ ?

Answer 1

Hint: So, this is our linear equation in two variables. Here, we have to find the value of ‘x’ by using a substitution method. In this case, we need to leave ‘x’ alone and take all the terms to the other side. After this, put different values for ‘y’ and check the value of ‘x’. For every single value of ‘y’ we will be able to find the corresponding value of ‘x’.

Complete step by step answer:
Now, let’s begin to solve the question.
First, let us write the equation as given in question:
$\Rightarrow y=5x+9$
Now, take 9 to the left-hand side. So, the equation will become:
$\Rightarrow y-9=5x$
Now, take 5 also on the left-hand side. 5 is in multiplication with x. After going left-hand side, it will be divided.
Let’s this step now:
$\therefore \dfrac{y-9}{5}=x......(i)$
So, finally we got the equation with the help of which we can easily find all the values of ‘x’ corresponding to the variable ‘y’.
Now, we will find some values of ‘x’ by placing some value of ‘y’ in the final equation.
Let’s place y = 4 in equation(i):
$\begin{align}
  & \Rightarrow \dfrac{4-9}{5}=x \\
 & \Rightarrow \dfrac{-5}{5}=x \\
\end{align}$
After cancellation we get:
$\Rightarrow x=-1$
Let’s see it graphically also that how it actually looks like:

See, it is visible that for y = 4 we are getting the value of ‘x’ as -1.
Let’s try one more input for y.
Now, let’s try with y = -1.
$\begin{align}
  & \Rightarrow \dfrac{y-9}{5}=x \\
 & \Rightarrow \dfrac{-1-9}{5}=x \\
 & \Rightarrow \dfrac{-10}{5}=x \\
\end{align}$
After cancellation:
$\therefore x=-2$
Let’s see it graphically once more that how it actually looks like now:

See, it is visible that for y = -1 we are getting the value of ‘x’ as -2.
Now, try yourself once. Put some value of ‘y’ and check the corresponding value of ‘x’.
So, finally make the table for all the values of x and y so that we should know what all values we got and we can easily plot the graph of it.

x	-1	-2
y	4	-1

Note: Students usually make mistakes by putting the values in ‘x’ and finding the value of ‘y’. So it is advised to solve according to the question. If they ask to find the value of ‘y’ then directly put the value of ‘x’ to find the value of ‘y’ otherwise do as directed above. Making a table of all the values in the end is not much necessary but will help you plot the graph easily and your solution will look neat.