Question

The work of a student to solve a set of equations is shown:

Equation A: y = 15 – 2z
Equation B: 3y = 3 – 4z

Step 1: –3(y) = –3(15 – 2z) [Equation A is multiplied by –3.]
3y = 3 – 4z [Equation B]
Step 2: –3y = 15 – 2z [Equation A in Step 1 is simplified.]
3y = 3 – 4z [Equation B]
Step 3: 0 = 18 – 6z [Equations in Step 2 are added.]
Step 4: 6z = 18
Step 5: z = 3


In which step did the student first make an error?



Step 4
Step 3
Step 2
Step 1

Answer 1

@satellite73

Answer 2

Try solving it yourself then see where he made the mistake.

Answer 3

HINT: start with substitution

Answer 4

i did! is step one wrong?

Answer 5

Yep xD

Answer 6

What did he do wrong?

Answer 7

so step one is the right answer?

Answer 8

Well yeah but what was his mistake?

Answer 9

he put a -3 instead of a 3

Answer 10

yea but one thing i dont understand why is there another y?

Answer 11

Are you sure Step 1 is wrong?

Answer 12

\[\huge~–3(y) = –3(15 – 2z)\]
it says y equals... 15-2z...

Answer 13

Yes but we're allowed to multiply both sides of an equation by -3

Answer 14

It says y=15-2z
the person never plugged it in place of y .

Answer 15

The problem says the student is working to solve the system of equations. There's more than one way to solve a system.

Answer 16

Multiplying both sides of an equation by -3 does not count as an "error". Nothing "wrong" was done in that step. The student approached differently than you would have.

Answer 17

Right but it looks like they used substituion.... :/ This is typed out weirdly .-.

Answer 18

so witch one would it be?

Answer 19

i'm confused now!

Answer 20

plz explain this to me!

Answer 21

anyone?

Answer 22

y = 15 – 2z
3y = 3 – 4z
how would u find the solution ?
you need same coefficient but opposite sign to isolate for one variable
that's why multiply 1st equation by -3
so -3(y = 15 -2z) = ???

Answer 23

@Hero is the answer step 4

Answer 24

Guessing is not the best approach to this. How'd you make it through the other steps successfully? The truth is you wouldn't even really need to ask which step is correct, if you had the correct approach. But I understand you're asking for help. So we know step 1 is correct. What are your thoughts on step 2?

Answer 25

i don't see anything wrong with step 2

Answer 26

So the equations in step 1 are equivalent to the equations in step 2? Because when solving systems, for each step, the equations have to all be equivalent.

Answer 27

im not sure

Answer 28

In step 1, for the first equation, after multiplying both sides by -3, we have:

–3(y) = –3(15 – 2z)

In step 2, that equation was supposedly simplified to get:

–3(y) = 15 – 2z

Tell me, is –3(y) = 15 – 2z equivalent to y = 15 – 2z ?

Answer 29

no

Answer 30

Why not?

Answer 31

becuase its -3y and the other one is plain y

Answer 32

So what does this observation tell you?

Answer 33

that step 2 is wrong. so step two is the answer

Answer 34

Bingo.

Answer 35

thanks for explaning.

Answer 36

You're most welcome.