A linear equation is an algebraic equation, such as y = 2x + 7 or 3x + 2y − z = 4, in which the highest degree term in the variable or variables is of the first degree. The graph of such an equation is a straight line if there are two variables.

Things you can do to solve linear equations:

You can add or subtract the same term from both sides of an equation.

Example: 

 -y + 5 = 17

-y + y = 17 + y    (add +y to both sides)

-y  + y = 0 = 17 + y

0 - 17 = 17 - 17 +y     (subtract 17 from both sides)

y = -17

You can multiply both sides of an equation by the same term; but remember, when you multiply each side, you must multiply each term in that side by the multiplier. You can also divide both sides of an equation by the same term, but you also must divide each term in that side by the dividing term

Example:

(5x - 4)/ 6 = 4 + 3x

5x -4 = 6(4 +3x) = 24 + 18x   multiply both sides by 6

-4 = 24 +18x - 5x   subtract 5x from both sides

-4 - 24 = 13x   subtract 24 from both sides

x = - 28/13   divide both sides by 13

An equation that is true for every value of its variable is called an identity.

Example: The equation 4(r+1) - 6 = 4r - 2 is true for all values of r.