Question

What is the solution to the system below?

-3x-y=-3
9x+3y=12
(3, 3)

(3, -3)

no solution

infinite solutions on the line

Answer 1

This is how you would solve it:
-3x-y = -3
9x+3y=12
If I simplify the 2nd equation a bit, I will get:
-3x - y = -3
3x + y = 4

Answer 2

Now:
Solve for 3x in the 2nd equation and plug it into the first one:
-3x - y = -3
3x = 4 - y

Answer 3

if you plug that into the first one, you will get:
- ( 4-y ) - y = -3
-4 + y - y = -3
-4 = -3
No solutions exist.

Answer 4

davette this is too long a solutions for this question
better check the ratios

a1 b1 c1
---- ---- ----
a2 b2 c2

IF a1 b1
---- not equal to ---- => one solution
a2 b2

If a1/a2 = b1/b2 = c1/c2 => infinite solutions

if a1/a2 = b1/b2 not equal to c1/c2 => no solution