Question

Solve the following system of equations.

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

Answer 1

The first equation gives us:
x+4y+z=-10
x=-10-4y-z

Answer 2

Next:
3x – 3y + 6z = –21
3(-10-4y-z)-3y+6z=-21
-30-12y-3z-3y+6z=-21
-3z+6z=15y+30-21
3z=15y+9
\[z=(15y+9)/3\]

Answer 3

Do you want the steps?

Answer 4

I'll just put the answers and noye can write it out
x=-4
y=-1
z=-2

Answer 5

x + 2y + 2z = –10
(-10-4y-(15y+9)/3))+2y+2(15y+9)/3=-10

Answer 6

basically you want to take the first equations and multiply it and add it to the second to cancel out one variable (preferably x) and then do it with the second equation replacing the equation you added the first equation with the new equation

Answer 7

later on you'll use it in matrices and call it reduced form

Answer 8

or Gauss eliminations i believe

Answer 9

So it's easier to solve those equations with matrices?

Answer 10

I have looked at them a little but I haven't used them yet.

Answer 11

much easier as Linear algebra and matrices all solve the same thing: Linear equations and this is a linear equation

Answer 12

Ok nice :)

Answer 13

i could solve this like 5 ways with matrices this is the simplest and the first way taught in Linear Algebra

Answer 14

If you are interested on like cool ways of doing this, look up cramer's rule ... you can use determinants to find x, y and z

Answer 15

Ok, I'll google it. Thanks for the help.

Answer 16

yep, Although her or your teacher (if you are the same person or in the same class) probably want you to do it without a matrix but essentially a matrix and the system of equations are the same thing

Answer 17

Augmented matrix*