Question

2. Solve the following system. Show all your work. {3x - 2y + 2z = 30 {-x + 3y - 4z = -33 {2x - 4y + 3z = 42

Answer 1

do you know the elimination method ?

Answer 2

know ABOUT it yes. but i don't really understand it all to well.

Answer 3

take any two of your equations and try to eliminate a variable. Sometimes you have to multiply an equation by a certain number to make the variable cancel out.

3x - 2y + 2z = 30
-x + 3y - 4z = -33 -->(3)
----------------
3x - 2y + 2z = 30
-3x + 9y - 12z = - 99 (result of multiplying by 3)
----------------add
7y - 10z = - 69

do you understand what I did so far ?

Answer 4

yeah!

Answer 5

now we will take the equation we didn't use and either of the other equations and eliminate x as well. Whatever variable we eliminate in the first two equations, we have to eliminate in the last two equations. So we have to eliminate x.

-x + 3y - 4z = -33 -->(2)
2x - 4y + 3z = 42
-----------------
-2x + 6y - 8z = - 66 (result of multiplying by 2)
2x - 4y + 3z = 42
----------------add
2y - 5z = - 24

you still with me ? Have any questions so far ?

Answer 6

yep! none so far!

Answer 7

Now we take the " answers " we got (the 2 equations that we eliminated x in), and add them together eliminating a variable.

7y - 10z = -69
2y - 5z = -24 -->(-2)
--------------
7y - 10z = -69
-4y + 10z = 48 (result of multiplying by -2)
-------------add
3y = -21 (divide by 3)
y = -7

Now we have solved a variable. You understanding so far ?

Answer 8

WOW! yep! your a great teacher!! I'm understanding it clearer now! Thanks!

Answer 9

now we will sub -7 in for y in one of the equation that we eliminated x in.

7y - 10z = -69
7(-7) - 10z = -69
-49 - 10z = -69
-10z = -69 + 49
-10z = - 20
z = 2

catching on now ?

Answer 10

yep

Answer 11

now that we know y and z, we will sub those answers into one of the original equations to find x.

-x + 3y - 4z = -33
-x + 3(-7) - 4(2) = -33
-x - 21 - 8 = -33
-x - 29 = -33
-x = -33 + 29
-x = - 4
x = 4

and now we will check our answers by subbing in what we got for the variables into one of the original equations. I suggest checking your answers because in elimination, mistakes can be easily made.

Lets check...
2x - 4y + 3z = 42
2(4) - 4(-7) + 3(2) = 42
8 + 28 + 6 = 42
14 + 28 = 42
42 = 42 (correct)

if it comes out equal, then your answers are correct.

x = 4, y = -7 and z = 2

any questions ?

Answer 12

nope you answered my question completely! thanks!

Answer 13

no problem :) I hope I made it easier for you to understand

Answer 14

Yes you did! Thanks again for taking the time!

Answer 15

thats what I am here for :)