Question

2x+2y-3z=-4
3y-z=-4
4x-y+z=4, solve by any method, can someone help me step by step

Answer 1

solve for one and plug it into the other keep doing that.

Answer 2

x = 1/2, y = -1, z = 1

Answer 3

what method do you know?

Answer 4

well none, but i kinda get the substitution method

Answer 5

the substitution method is one way but this being a 3x3 system, it might get messy.
when you did 2x2 systems, do you remember elimination?

Answer 6

not really, like i know the answer i just need to see the steps

Answer 7

i can show the steps in elimination if you like...

Answer 8

ok please

Answer 9

ok... elimination means you will be eliminating a variable so you have less to work with...
this is the way it works with a 3x3 system..
3x3 system ---> eliminate variable --->2x2 system ---> eliminate variable ---> 1x1 system or 1 equation with 1 variable.

Answer 10

so we need to work our way down to 1 equation with 1 variable to solve the 3x3 system...

Answer 11

notice the middle equation only has two variables so we can use that as one of our equations in our 2x2 system.

Answer 12

still with me?

Answer 13

yess

Answer 14

ok so can we work together on the problem that i need help with

Answer 15

that middle equation has the variables y and z... so if we can "combine" the first and last equations by eliminating x, we'll end up with 1 equation with the variables y and z...

Answer 16

notice in A, i'm only working with the first and last equations. i'm gonna eliminate the "x" variable by multiplying the first equation by 2, then subtract the third equation...