# Equivalent Linear Equations

- Author:
- Lew W. S.

- Topic:
- Algebra, Equations, Linear Equations

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.