Question

Help! Solution problems ): Difficult for me
-3x - 2y = -12
9x + 6y = -9
and
x - y = 11
-x + y = -11

Answer 1

You can solve this by method of substitution. You do this by taking one of the equations and "isolating" either x or y. we'll start with your top problem. If you isolate x you get:

x=4-(2/3)y

After you isolate one of the variables you simply "substiute" what you got into the second equation. So you plug x into the second equation. If you do this you get:

9(4-(2/3)y)+6y=-9

At this point you just solve for y. When we try to simplify the left side, though, y ends up disappearing. So you get something that looks like this:

36=-9

Since we know this is not true, this problem has NO SOLUTION

Doing a similar approach to your 2nd problems yields:

-11=-11

This answer is true but the x and y variables disappeared! This means that the answer is "infinitely many solutions"

Answer 2

-3x - 2y = -12-->(3)
9x + 6y = -9
---------------
-9x - 6y = - 36 (result of multiplying by 3)
9x + 6y = -9
----------------add
0 = - 45 (incorrect)

I do not believe there is a solution to this problem
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x - y = 11
-x + y = -11
--------------add
0 + 0 = 0

This has infinite solutions