Linear Equations

Linear Equations

An equation that can be written of the form

where and are (fixed) real numbers and is the variable (or the unknown) is called a linear equation. To solve the equation, subtract from both sides

and then divide both sides of the resulting equation, , by :

(Sometimes, this process is described as "transferring to the other side of the equation and then "moving the coefficient to the denominator of ".)

  • The solution of is the -intercept of the straight line (the -intercept is where the graph intersects the -axis).

Solve:

Solution We first simplify and then rewrite the equations of the form that all terms containing the variable are on one side and the constant terms are on the other side.

Solve

Solution To clear of fractions, multiply both members by the LCD, 6 . Then or Transpose and collect terms, . Therefore Verfication:

Solve .

Solution Double subscripts: use braces to clarifyLCD_=_12" transform="translate(3453.4,3345)">_to_and_subtract__from_both_sides" transform="translate(0,-1254.5)">" transform="translate(8112,-4446.5)">