# Equivalent Linear Equations

Author:
Lew W. S.
Practice manipulating linear equations from one form to another, as equivalent linear equations. Linear equations are equivalent when their solution for the unknowns are the same. For example y = 2x - 1 2y = 4x - 2 (multiplied both sides of the equation by 2, thus keeping it balanced equally) -4x + 2y= - 2 (subtracted 4x from both sides of the equation) -4x + 2y + 2 = 0 (added 2 to both sides) -2x + y + 1 = 0 (divided both sides by 2) y - 2x + 1 = 0 (moved term in y in front of term in x) The equations y = 2x - 1, 2y = 4x - 2, -4x + 2y = - 2, -4x + 2y + 2 = 0, -2x + y + 1 = 0 and y - 2x + 1 = 0 are all equivalent equations. They are written in different forms y = 2x - 1 is in the form y = mx + c where m is the gradient and c is the y intercept -4x + 2y = -2 is in the form ax + by = c where a, b and c are integers -2x + y + 1 = 0 is in the form ax + by + c = 0 where a, b and c are integers. Do the practice below to master your algebraic skills in obtaining equivalent linear equations.