Question

Thank you :)

Answer 1

Yeah...it looks like you already know that 'y' is supposed to equal 3?

Answer 2

Hang on...is that

\[-x + \frac{2}{9y} = 1\]
or
\[\frac{-x + 2}{9y} = 1\]
or
\[-x + \frac{2}{9}y = 1\]

Answer 3

The 3rd one

Answer 4

Alright that makes sense...hang on 1 sec...

Answer 5

So the trick with elimination problems, is you're supposed to multiply either the top, or bottom (or both sometimes) equation by something so that when you combine (add) the 2 equations...one variable cancels and you can solve...so lets solve for y since you know it equals 3

-x+(2/9)y=1
9x+3y=6

if we multiply the top equation by 9...it looks like when we add -9x and 9x they will cancel out right? so lets do that...

9(-x + (2/9)y = 1)
becomes
-9x + 2y = 9

so now we have

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

Lets add the 2 equations

-9x + 2y = 9
+( 9x + 3y = 6)
----------------
5y = 15

Now just divide both sides by 5 to get

5y = 15
--------
5 5

y = 3

Which you have as correct

Answer 6

Does that make sense?

Answer 7

Oh...when you plug in 3 for the 'y' ?

Well okay...

so the first equation...

-x+(2/9)y=1

Replacing y with 3

-x+(2/9)(3)=1
-x+(6/9)=1
-x + (2/3) = 1
-x = 1 - (2/3)
-x = 1/3
x = -(1/3)

So you have it correct!

Here we can check in the second equation...

We now know that y = 3 and x = -1/3

so

9x + 3y = 6

9(-1/3) + 3(3) = 6
-9/3 + 9 = 6
-3 + 9 = 6
6 = 6 <---correct :)