How do you write linear equations?

Answer 1

Linear equations take the form y= mx+b where

m is the slope [rise(y)/run(x) on a graph]

x is the x-value any point on the graph

y is the y-value of any point on the graph

b is the y-intercept on the graph

Linear equations take the form a1x1 + a2x2 + a3x3 + ... + anxn + an+1 = 0

Each ai represents a constant, xi a variable.

The equation above is linear in n dimensions. In two dimensions, linear equations are typically written ax + by = c. In three dimensions, ax + by + cz = d. After that, the form given above (with the subscripts) is preferred.

Any system of n equations and n unknowns may have a unique solution. If two of the equations are multiples of each other, the solution set will not be unique, but represent a line, plane, or subspace. It is also possible the system may have no solution, such as the following:

5x + 10y = 5

5x + 10y = 20

This system represents two parallel lines--there is no solution.