Question 6(multiple choice worth 5 points) (8.05 hc) 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

Explanation:

Here, I copy each step given and review them algebraically, until finding the first error made by the student.

0) Start: System of equations:

1) Step 1:

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

 2y = 3 − 4z [Equation B]

This procedure is algebraically correct, since the student used correctly the multiplicative property of equalities: both sides of the equation A are multiplied by the same number, 2.

Whereas, the equation B is not algebraically manipulated.

2) Step 2:

This procedure is algebraically wrong, since the student applied wrongly the distributive property of multiplication to simplify the equation A:

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

                     -2y = - 30 + 4z

Conclusion: The studend made an error in the second setp, since he/she did not apply the distributive property correctly.

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

step-by-step explanation:

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