The work of a student to solve a set of equations is shown:
Equation A: y = 10 - 22
Equation B: 5y = 2 - 4z
Step 1: -5(y) = -5(10 – 2z) [Equation A is multiplied by -5.]
5y = 2 - 42 [Equation B]
Step 2: _5y = 10-22 [Equation A in Step 1 is simplified.]
5y = 2 - 4z [Equation B]
Step 3:
0 = 12 - 6 [Equations in Step 2 are added.]
Step 4:
z = 12
Step 5:
z = 12
In which step did the student first make an error?

Equation B: 5y = 2 - 4z solved by a student, we are to determine the step where the student made an error in his/her calculation. Let's follow the steps;

Step 1: multiply equation A by -5. The essence of this is to be able to cancel out one of the variables and calculate for the other variable. On multiplication we have;

y = 10 - 2z × (-5)

5y = 2 - 4z × (1)

_____________________

-5y = -5(10-2z) .... A

5y = 2 - 4z..... B

Step 2: simplify equation A by opening the bracket.

-5y = -5(10)+5(2z)

-5y = -50+10z

The equations become;

-5y = -50+10z .... A

5y = 2 - 4z..... B

It can be seen that her simplified expression does not tally with what we got i.e -5y = -50+10z. This was the step the student made the first error.

Since this student step is wrong, the remaining calculation will be wrong.

Let us fix the calculation steps now.

We will continue from the previous step.

Step3: Add equation A and B in step 2 together.

-5y+5y = (-50+2)+(10z-4z)

0 = -48+6z

Step 4: Add 48 to both sides:

0+48 = -48+6z+48

48 = 0+6z

48 = 6z

Step 5: Divide both sides by 6

48/6 = 6z/6

6 = z

z= 6

Hence, the value of z = 6 not 12 and the student made his/her first error in step 2.