Question

Solve:
2x + 3y - 2z = -3
x + 9y - 2z = 3
3x + 6y + 2z = -1

I've tried pretty much every tactic I know to work this, can't figure it out. If someone could go step by step, that would help me out a lot.

Answer 1

divide second eqn by 3
and divide third eqn by 2

Answer 2

so u will get 3y in all eqns thn add em

Answer 3

Substitution is the coolest! =D
Pick your favorite equation and your favorite variable. Solve for that variable. Plug into either of the OTHER two equations. That gets you an equation with only 2 variables.
Solve that equation for one of the remaining variables, plug into the 3rd equation.

Answer 4

u can use Matrix to solve this, try it

Answer 5

Smooth: That's what I did. But I came up with 5x + 9y = -4 and 4x + 15y = 2 and those two can't be multiplied in any form to just get x or y.

Answer 6

hey linux have u tried the matrix approach , very simple & solvable

Answer 7

Can't they though, Linux?

Answer 8

I don't know what the matrix approach is. Lol.

Answer 9

2x + 3y - 2z = -3
x + 9y - 2z = 3
3x + 6y + 2z = -1

solving the second equation for x:
x = -9y +2z +3
substituting that into the first equation
3(-9y+2z+3)+3y-2z = -3
-24y + 4z =-12

Solving that for z gives
z = -3 + 6y
and plugging into the third equation for both x and z gives:
3x + 6y + 2z = -1
3(-9y +2z +3) + 6y +2(-3+6y) = -1
3(-9y +2(-3+6y)+3)+ 6y +2(-3+6y) = -1

Answer 10

Before I continue, do you see what I've done so far?

Answer 11

Yes, makes perfect sense now.

Answer 12

That last step is especially tricky. You're sure you see how I substituted in for x and then for z twice?

Answer 13

And that gives us a big messy equation, but it only has y in it, so we can solve it no problem.

Answer 14

Yes, when I working it I was trying to solve for x or y, but it wasn't working right,

Answer 15

Hmm. I'd love to see your work so that I could help you see your mistake.

Answer 16

You should be able to solve for any variable you choose.

Answer 17

Well, I took a and c first which gave me 5x + 9y = -4 and then I did b and c which gave me 4x + 15y = 2 then I tried went to put them together so I could change one and add them and then eventually solve for x, but I can't figure out how, since they can't be multipled in a way I can see.

Answer 18

Ah, wait. I think I got the answers. x = -2 y = 2/3 and z = 1/2

Answer 19

You can actually use those two equations, but it would require some fraction work.

5x+9y = -4
4x + 15y = 2

Solving equation 1 for x gives
x = (-4/5) -(9/5)y
substituting into equation 2 gives
4((-4/5)-(9/5)y) + 15y = 2
(-16/5)-(36/5)y + 15y = 2
(-16/5)+(39/5)y = 2
(39/5)y = 26/5
y = 26/39

Answer 20

and 26/39 = 2/3

Answer 21

So then my answers are correct?

Answer 22

Yes! Good work =)