An equation is a relation which states that two expressions are equal, identical, or otherwise the same. Equations are easily identifiable because they are composed of two expressions with an equals sign ('=') between them.
It's important to note the distinction between an equation and an identity. An identity in terms of some variables states that two expressions are equal for every value of those variables: for example,
is an equation that is true for some particular values of .
In other words, one can say that an identity is a tautological equation
A linear equation is the simplest form of equations (with one or more variables). It has the form , where are numbers and are the variables. In linear equations, the variables are never squared or cubed as in quadratics or cubics. The graph of a linear equation is always a straight line. Some examples of linear equations are the following:
How to solve a linear equation with one variable
Linear equations with one variable are of the form , where are numbers and is a variable. The common recipe for solving linear equations with one variable is the following:
Solve the equation
1. (We have to distinguish the terms. On the right side we put the variable terms and on the left side we put the numbers.)
2. (In order to achieve it, we have to add or subtract in both hand sides.)
3. (Now we have to convert the equation into the form . We shall proceed to divide both sides by .)
Hence the solution to our equation is .
How to solve a linear equation with multiple variables
Solve for and in the two equations and
1. Solve for y in terms of x
2. Substitute the value into the other equation and solve
3. Substitute the value of x back in
A quadratic equations highest exponent is two no less and no greater.