Question

Can someone please help me in Algebra II? I don't understand the substitution method. I have a couple problems I need help with. Thanks!

Answer 1

Use the substitution method to solve the following system of equations.

x + 2y – z = 2
3x + y – 2z = –15
3x + 4y – 3z = –2

Answer 2

@amistre64

Answer 3

@phi

Answer 4

for more than 2 variables, I don't like substitution.... do you have to do substitution ?

Answer 5

Yes, unfortunately...

Answer 6

ok, can you solve for x in the first equation ?

Answer 7

I don't know how to...

Answer 8

There are two other variables... How would I solve for x?

Answer 9

"move" the other terms to the right-hand side of the = sign
to move the 2y add -2y to both sides
to move the -z add +z to both sides

what do you get ?

Answer 10

2-2y+z

Answer 11

yes, but you should write it as
x = 2-2y+z

because solving this mess means being very careful, and writing everything down
(I lose track if I don't)

now replace x with (2-2y+z) in the other two equations
can you do that ?

Answer 12

I think so

Answer 13

or just multiply that by 3 an replace the whole 3x shebang

Answer 14

3(2-2y+z)+y-2z=-15
and
3(2-2y+z)+4y-3z=-2

Answer 15

next, for both equations ,
distribute the 3 and then combine "like terms"

can you do that ?

Answer 16

yeah

Answer 17

-5y+z=-9
and
-2y=4

Answer 18

-2y=-8?

Answer 19

almost. I think after distributing the 3 you get (in the first equation)
6 -6y + 3z + y -2z = -15
combine -6y + y to get -5y
combine 3z -2z to get +z
6 -5y + z = -15

add -6 to both sides to get
-5y + z = -15-6 = -21

can you redo the 2nd equation ?

Answer 20

yes, so you have
-5y + z = -21
-2y = -8

now solve for y. I would use the 2nd equation (for obvious reasons)

Answer 21

y=4

Answer 22

now use y=4 in the other equation
-5y + z = -21
and solve for z

Answer 23

-1?

Answer 24

finally use y=4 and z=-1 in
x = 2-2y+z

Answer 25

-3?

Answer 26

how ?

Answer 27

wait... is it 7?

Answer 28

or -5..? I'm confused...

Answer 29

don't lose the bubble... start with
x= 2 - 2*y + z
replace y with 4
x = 2 - 2*4 + z
replace z with -1

x= 2 - 2*4 + -1

what is x?

Answer 30

-7

Answer 31

so that is the answer
x= -7, y=4, z=-1

as a quick check, see if the 1st equation works:
x + 2y – z = 2

-7 + 2*4 - (-1) = -7 + 8 + 1 = 1+1= 2

so 2 = 2 is true and it works

Answer 32

Thank you so much! I feel like I actually understand how to solve these! Is there any way you can help me with one more thing? I don't know how to convert a word problem into a system of equations like this... I have an example

Answer 33

please make it a new post

Answer 34

ok