# Solution Of An Equation

Equations are mathematical statements that say that two (2) expressions are equal. Expressions are mathematical phrases that may contain a combination of variables, numbers, or operations.

Let’s begin with the proper definition of what a variable is. Variables are symbols (usually letters) that stand for values that may vary. What follows next is the proper definition of equations.

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1. Is 8 a solution of $$5 = 12 - y$$?
A.
B.

Question 1 of 2

2. Is $$43$$ a solution of the equation $$4 = y - 39$$?
A.
B.

Question 2 of 2

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Next Lesson: Equivalent Equations
This lesson is a part of our GED Math Study Guide.

### Video Transcription

Equations are mathematical statements that equate two (2) mathematical expressions. It’s quite simple: the main difference between mathematical expressions and equations is whether there’s an “equals” sign or not.

For example:
Both x + 2y + 3 and x + 2x – 3 are actually mathematical expressions, while x + 3 = 4 and x = 9 are our equations.

Next, we’ll look at the proper definition of what the solution of an equation is, what it means to be a Solution.

Solutions of equations are numerical values that satisfy the equation. This is when variables in the equations are replaced by our solutions, true statements result.

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Here is our example number one: Show that the number 3 is a solution to our equation x + 8 = 11.

The solution is: substitute 3 for x in our equation and then simplify.
x + 8 = 11
3 + 8 = 11
Since both the left side and the right side of this last line are equal, it demonstrates that when we substitute x for the number 3 in our equation, the result is a true statement.

Therefore, the number 3 is a solution to our equation.

Now, example number two: Is 23 a solution of equation 4 = y − 11?

4 = y − 11
Substitute 23 for y.

4 = 23 − 11
4 = 12

Because the left side and the right side of this last line are not equal, this demonstrates that when we substitute y for 23 in our equation, the result is a false statement. Therefore, the number 23 is not a solution to our equation.