# Solving Linear System of Equations: Elimination

1. Sep 2, 2012

### ilovecake

1. The problem statement, all variables and given/known data

A general system of linear equations is
ax+by=e
cx+dy=f

where a,b,c,d,e,f are constant values.

a)Use elimination to solve for x and y in terms of a,b,c,d,e,f.

b)Are there any values that a,b,c,d,e,f cannot have?

3. The attempt at a solution

For part A, I got x=(e-f)/(a-c), assuming using subtraction for elimination, but in the answers it says x=(de-bf)/(ad-bc). Why are the coefficients of y there?

For part B, I think ad=/=bc because then both equations would cancel out, and it is either the exact same equation or has the same slope but parallel and never intersecting.

for example, 15x+9y & 5x+3y

Last edited: Sep 2, 2012
2. Sep 2, 2012

RGV

3. Sep 2, 2012

### ilovecake

using elimination by subtraction, solving for x:
ax+by=e
cx+dy=f

(ax+by)-(cx+dy)=(e-f)
ax-cx +by-dy=(e-f)
(a-c)x=(e-f)
x=(e-f)/(a-c)

Nevermind, I just realized that it's to make the coefficients of y the same.