Question

What is the solution of the following system?

Answer 1

@redshift

Answer 2

Last one for me today.

I'll solve this one with substitution.

-3x - 2y = -12,
9x + 6y = -9

So I'll randomly pick one and isolate for either x or y. Want to try first? I'll help you through it.

Answer 3

6x + 4 = -21

Answer 4

6x = -25

Answer 5

hmm, how did you get there?

Obviously you chose to isolate for x but from which equation?

What I did:

-3x - 2y = -12

add 2y to both sides:
-3x - 2y + 2y = -12 + 2y
-3x = -12 + 2y

divide both sides by -3:
(-3x)/(-3) = (-12 + 2y)/(-3)

This is the same as:
x = (-12/-3) + (2y/-3)

So,
x = 4 - (2/3)y

Answer 6

ugh why cant i be as smart as you but i dont get it none a b c or d are that answer

Answer 7

This question is tricky/interesting:

Now I take that x and put it into the other equation:
9x + 6y = -9
9(4 - (2/3)y) + 6y = -9

distribute the 9:
45 - 6y + 6y = -9
45 = -9!!

Weird eh. But this is actually what I expected.

Answer 8

hmmm :\

Answer 9

There is actually no solution :)

If you rearrange them, you'll find they actually have the same slope!

-3x - 2y = -12 -> y = -(3/2)x + 6
9x + 6y = -9 -> y = -(3/2)x - (3/2)

notice m = -(3/2) in both!

So they are actually parallel and never intersect.

See the attached graph:

Answer 10

Don't be discouraged! I wasn't always this good :)

So a few things to remember:

If the two lines cross in only one spot: Then there is ONE solution.

If the two lines are parallel(never touch): Then there are ZERO solutions.

If the two lines are the same(touch everywhere): Then there are an INFINITE number of solutions.