the solution checks i do are not the way teracher wants them?

Question

3x + 4y = - 13
3x= -13 – 4y
x = 13/3 – 4y/3

5y - x = - 21
5y – (- 13/3 – 4y/3) = - 21
5y + 13/3 + 4y/3 = - 21
5y + 4y/3 = - 21 – 13/3
15y+4y/3 = - 63 –13/3
19y/3 = - 76/3
19y = - 76
y = - 76/19 = - 4

x= 13/3 + 4/3 * 76/19 = -1/3( 13 - 4*76/19) = -1/3 (247-304)/19 = 1

The Solution set is ( 1, -4)

How would anyone else do this, besides just plugging in the "known?" gee willikers

Answer 1

I would use Cramer's Rule, see
http://en.wikipedia.org/wiki/Cramer's_rule
or
http://www.purplemath.com/modules/cramers.htm

It's harder to explain than it is to do.

Answer 2

x = -13/3 – 4y/3

15y+4y = - 63 –13