Question

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?
a: Step1
b: Step 2
c: Step 3
d: Step 4

Answer 1

It is B. Step 2

Explanation:

Answer 2

Option B. Step 2

Explanation:

we have

`y=15-2z` ----> equation A

`2y=3-4z` ----> equation B

step 1

Multiply equation A by -2 both sides

`-2(y)=-2(15-2z)`

step 2

Simplify equation A

`-2(y)=-2(15-2z)`

`-2y=-30+4z` -----> equation A

The first error is in step 2

The student's mistake was to multiply equation A by -2 on the left side only and not on both sides.

step 3

Adds equation A and equation B

`-2y=-30+4z\\2y=3-4z\\---------\\0=-30+4z+3-4z\\27=0`

The system has no solution

The lines are parallel