Can someone please help me, this is my last question I have been stuck on it for 30 min



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


Equation A: y = 15 − 2z

Equation B: 2y = 3 − 4z



Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]

2y = 3 − 4z [Equation B]

Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]

2y = 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?

Step1

Step 2

Step 3

Step 4

Verified Answer :

step 2
he didn't distribute
what he did:
-2(15-2z)=15-2z
that is obviously false

what should have happened is
-2(15-2z)=-30+4z
then add

-2y=-30+4z
2y=4-4z
0=-26
false
no solution
inconsitient, these lines ar paralell


anyway, step 2 is error

The mistake was made in step 2.  In simplifying the equation, he has to distribute the -2 through the parentheses.  Step 2 simplification should be

-2y = -30 + 4z

When the 2 equations are added, the resultant equation is 0 = -27 therefore it has no solution.