Subtitute for a Variable - Definition & Examples

(Video) Substituting Numbers for a Variable

by Skarinsensei

Here's a video by Skarinsensei that shows you what to do when substituting a number into a variables place.

$\large{\text{Summary}}$

You can substitute a variable for any given number, a constant. You can take an expression or equation, with a definition for a variable, and plug that definition in. Let's look at an example:

What is $x-1$ when $x=3$?

We're going to plug in $3$ for $x$, then calculate our answer. $$\begin{align}x-1&=\\ {\color{#8925AE}{3}}-1&=2 \end{align}$$

Let's take a look at a harder example: $$x^2+3x+2$$ What does this expression equal when we substitute in $x=5$?

Start by plugging in $5$ for every $x$. $$\begin{align} &x^2+3x+2\\ &=({\color{#8925AE}{5}})^2+3({\color{#8925AE}{5}})+2 \end{align}$$

Then, simplify! $$\begin{align} &=5^2+3(5)+2\\ &=25+15+2\\ &=42 \end{align}$$

You may come across a situation when you need to use PEMDAS (order of operations) to solve the problem. In that case, first plug in the $x$ value, and then use PEMDAS to solve the equation or expression like normal.

You can also use this method when solving more complex equations, like equations with fractions or equations with decimals. You can also use this method to double check solved solutions.

We're going to plug in $5$ anywhere we see $x$. $$\begin{align}x+7&=\\ {\color{#8925AE}{5}} +7 &= 12 \end{align}$$

Substitution is an essential part of solving equations for variables. Variables (like $x$, $y$, $z$) are stand-ins for constants ($-4$, $\frac{2}{3}$, $\pi$), plugging the constant back into the equation is a great way to check your work. This concept is also very important when you want to solve a system of equations!

Let's look at an example!

We want to isolate $x$ on one side of the equation. Once we have a value for the variable, we can plug the value into the equation to test if our answer is correct.

Since we end up with something true, we know that we solved correctly for $x$ in the first place!

You may also want to use this method to find the corresponding $y$ value for the $x$ value. You'll need to substitute to solve the equation. If you're looking for a slightly less precise way to find the corresponding $y$ value, you can also estimate values by graphing.

If we think back to the definition of variable, we know that it's a placeholder for numeric values. Generally, a variable can take on a range of values, unless otherwise specified.

Say we were given an algebraic equation, and we wanted to solve for one specific value. How would we do that?

We can substitute a numeric value in for the variable, in this case $x$, and solve as normal.

Let's do an example.

Solution: When $x=3$, $$2x+5$$ $$2(3)+5$$ $$6+5$$ $$11$$