An equation is a mathematical statement that has two expressions separated by an equal sign. The expression on the left side of the equal sign has the same value as the expression on the right side.
Example:
x = y
This means that both x and y has the same value
One or both of the expressions may contain variables.
If we add the same number to both sides of an equation, both sides will remain equal.
Example
Equation: x = y
Adding 5 to both sides
x + 5 = y + 5
If we subtract the same number to both sides of an equation, both sides will remain equal.
Example
Equation: x = y
Adding 5 to both sides
x - 5 = y - 5
If we multiply the same number to both sides of an equation, both sides will remain equal.
Example
Equation: x = y
Multiplying 5 to both sides
x * 5 = y * 5
5x = 5y
If we multiply the same number to both sides of an equation, both sides will remain equal.
Example
Equation: x = y
Dividing 5 to both sides
x ÷5 = y ÷5
For example solve the equation:
8x - 2 = 14
To keep both sides of an equation equal, we must do exactly the same thing to each side of the equation.
First, add two to each side of the equation so that...
8x - 2 + 2 = 14 + 2
8x=16.
If we multiply (or divide) one side by a quantity, we must multiply (or divide) the other side by that same quantity.
In order to solve this equation, we would divide both sides by 8.
The equation would become...
8x/8 = 16/8.
When simplified, this would become...
x = 16/8 or x = 2.
It is possible to substitute the value of x back into the original equation
8*2 - 2 = 14
Solving equations with more than one variable requires a set of equations, called a system of equations. Typically, the same number of equations should equal the number of variables; if there are 4 variables, the number of equations in the system usually would be 4.
In a "system of equations," you are asked to solve two or more equations at the same time. When these have two different variables in them, such as x and y, or a and b, two separate equations in x and y,( or a and b) will be given.
There are three ways to solve systems of linear equations:
Substitution,
Elimination, and
Graphing