Question

Can someone please help me find the solution to the systems of equations:
3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1
I'm looking for an explanation because I have been stuck on this question.

Answer 1

Okay, you can use elimination with the first and third equation. Subtract those 2 and tell me what you get.

Answer 2

I got 2z=6

Answer 3

It should be -2z=6
Solve for z.

Answer 4

Okay, z=-3

Answer 5

Okay, no rewrite all three of the equations but with -3 for z.

Answer 6

3x+2y-3=7
5x+5y-12=3
3x+2y-9=1

Answer 7

@Seratul

Answer 8

Simplify each equation.

Answer 9

3x+2y=10
5x+5y=15
3x+2y=10

Answer 10

Okay, take the second equation and isolate the y. Make sure you divide by 5 at the end.

Answer 11

y=-x+3

Answer 12

Wait, my bad, just divide by 5.

Answer 13

Is that correct?

Answer 14

I meant to say just divide by 5 so it should be
x+y=3
If you multiply by 2, you get
2x+2y=6
Now you can subtract
3x+2y=10 and
2x+2y=6.
Tell me what you get.
We are doing this so we can eliminate a variable.

Answer 15

Okay so, x=4

Answer 16

Yep. Now plug in both x and z and find y.

Answer 17

3(4)+2y-3=7
12+2y-3=7
9+2y=7
2y=-2
y=-1
?

Answer 18

Yep. There you go.

Answer 19

Great, thank you so much for the help!

Answer 20

np