Question

Solve the following system of equations.

x + 4y + z = -10
3x - 3y + 6z = -21
x + 2y + 2z = -10

Answer 1

A. (1, -2, -3)
B. (-4, -1, -2)
C. (-3, -2, -3)
D. (2, -2, -4)

Answer 2

How would i do this?

Answer 3

@dan815 @pooja195

Answer 4

If you don't know how to do a system of equations you can always just plug each of the coordinates into all 3 equations and see which one works lol

Answer 5

But anyway when you have 3 systems 3 variables, you want to try to turn it into 2 systems 2 variables.

Answer 6

1. x + 4y + z = -10
2. 3x - 3y + 6z = -21
3. x + 2y + 2z = -10

For equations 2 and 3, you can multiply equation 3 to get: 3x + 6y + 6z = -30

Then subtract equation 2 from 3 or 3 from 2. It doesn't really matter.
You get: 9y=-9

Thus, y=-1.

Since y=-1 this then turns your 3 systems 3 variables into 2 systems 2 variables.

Check if I did my math wrong. You should be able to do the rest.

Answer 7

@q12157 I like how you solved the problem, but it actually would matter for subtracting equation 2 and 3 or 3 and 2. Why? Well, this is what happens:
2. 3x - 3y + 6z = -21 -> 3x - 3y + 6z = -21
3. 3(x + 2y + 2z = -10) -> 3x + 6y + 6z = -30
Alright, subtraction:
3x - 3x or 3x - 3x = 0, however -3y - 6y = -9y, but 6y - -3y -> 6y + 3y = 9y, then there's 6z - 6z or 6z - 6z = 0. Finally: -21 - -30 -> -21 + 30 = 9, otherwise -30 - -21 -> -30 + 21 = -9.
You are right however, y = -1 regardless. Anyhow, I just wanted to point that out.
Have a great rest of your day! ;)
{---Ghostgate---}

Answer 8

Thats kinda what I meant. That it would be y=-1 regardless. Perhaps I didn't write it out too clearly haha.

Answer 9

Perhaps, well you explained it quite well nevertheless. ;) - Lol