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 .

y = 3x + 2 → 3x + y = 2
6x – 2y = 10 → 3x – y = 5
6x = 7
x =

6x – 2y = 10 → 6 – 2y = 10

7 – 2y = 10
–2y = –3

y = -

Jesse’s answer:
I used matrices. The solution is .



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

Answer 1

6x - 2y = 10

-2y = -6x + 10

reduce by dividing by -2

y = 3x - 5

slope = 3 and y int = -5

y = 3x + 2

slope = 3, y int = 2

These lines are parallel. Parallel lines will have the same slope, but different y integers. There is no solution to this because the lines never intersect.

Mark's answer is correct

Answer 2

6x - 2y = 10
-2y = -6x + 10...reduce by dividing by -2
y = 3x - 5....slope = 3 and y int = -5

y = 3x + 2 ...slope = 3, y int = 2

These lines are parallel. Parallel lines will have the same slope, but different y int's. There is no solution to this because ur lines never intersect.

Mark's answer is correct