Ryan, Jessica, and Mark each solved this system of equations. All of their answers are different. Find and explain the mistakes. What is the correct answer?

y = 3x + 2
6x – 2y = 10

Ryan’s answer:
I solved by adding the equations. The solution is (7/6, -3/2)

y = 3x + 2→ 3x + y = 2
6x – 2y = 10 → 3x – y = 5
6x = 7
x = 7/6
6x – 2y = 10→ 6(7/6) – 2y = 10
7 – 2y = 10
–2y = –3
y= -3/2

Question

Ryan, Jessica, and Mark each solved this system of equations. All of their answers are different. Find and explain the mistakes. What is the correct answer?

y = 3x + 2
6x – 2y = 10

Ryan’s answer:
I solved by adding the equations. The solution is (7/6, -3/2)

y = 3x + 2→	3x + y = 2
6x – 2y = 10 →	3x – y = 5
6x       = 7
x = 7/6
6x – 2y = 10→ 6(7/6) – 2y = 10
7 – 2y = 10
–2y = –3
y= -3/2

anonymous · Answer

Jesse’s answer:
I used matrices. The solution is (7/6,7/2)

anonymous · Answer

Mark's Answer: I graphed the equations. The lines are parallel and do not intersect, so there is no solution.

anonymous · Answer

I had graphed the original system of equations and Mark's answer is correct but I do not know the errors in the other two answers and need help finding them.

knov · Answer

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