Question

If you were to use the elimination method to solve the following system, choose the new system of equations that would result after the variable z is eliminated in the first and third equations, then the second and third equations.

x – y + 2z = –2
2x + 2y + z = 7
3x + 3y – z = 3

Answer 1

to eliminate z in the first and third equations, you have to multiply the entire third equation by 2

Answer 2

then add them together

Answer 3

so it would be
6x+6y-2z=6

then what do you mean by add them together?

Answer 4

x - y +2x = 2
+
6x + 6y -2z = 6

=

7x +5y = 8

z's cancel

Answer 5

now, to eliminate z in the second and third equations, just add them together

Answer 6

that shouldn't be a 2x in the first equation, it should be 2z

Answer 7

wrote 2x by accident ><

Answer 8

A. 2x + 2y = 7
3x + 3y = 3

B. 2x + 2y = 7
5x + 5y = 10

C. 7x + 5y = 4
3x + 3y = 3

D. 7x + 5y = 4
5x + 5y = 10

Answer 9

these are my only answers to choose from though?

Answer 10

when we added the first equation, x - y + 2z = -2, not 2, so when we added it the third equation, we should have gotten 4

Answer 11

have to be careful with the signs

Answer 12

so which one is the answer then?

Answer 13

cause im soo confused

Answer 14

our goal is to eliminate z. all we did to eliminate z for the first and third equations was
first: multiply the third equation by 2, so we could get -2z to cancel with +2z in the first equation

that gave us:

x - y + 2z = -2
+
6x +6y -2z = 6

= 7x + 5y = 4

Answer 15

do you understand that part?

Answer 16

okay .. get that part now.

Answer 17

what do we do next?

Answer 18

now, to eliminate z in the second and third equations, all we have to do is add them, since the z's will cancel

2x + 2y + z = 7
+
3x + 3y – z = 3

= ???

Answer 19

5x + 5y = 10

Answer 20

good job

Answer 21

which means it would be
D. 7x + 5y = 4
5x + 5y = 10

Answer 22

Thanks so much for your help!

Answer 23

yw