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?
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Try solving it yourself then see where he made the mistake.
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i did! is step one wrong?
What did he do wrong?
so step one is the right answer?
Well yeah but what was his mistake?
he put a -3 instead of a 3
yea but one thing i dont understand why is there another y?
Are you sure Step 1 is wrong?
\[\huge~–3(y) = –3(15 – 2z)\]
it says y equals... 15-2z...
Yes but we're allowed to multiply both sides of an equation by -3
It says y=15-2z
the person never plugged it in place of y .
The problem says the student is working to solve the system of equations. There's more than one way to solve a system.
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.
Right but it looks like they used substituion.... :/ This is typed out weirdly .-.
so witch one would it be?
i'm confused now!
plz explain this to me!
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) = ???
@Hero is the answer step 4
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?
i don't see anything wrong with step 2
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.
im not sure
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 ?