Question

Three students are working to find the solution set of this system of equations:

3y = 6x + 6
y = 2x + 2
Use the drop-down menus to complete the statements about each of their methods.


Pedro Dropdown 1: Intersect, Do not Intersect, Are the same line.

Pedro Dropdown 2: One, Zero, Infinitely many

Amy Dropdown: is, is not

Matt Dropdown 1: Sometimes, Never, Always

Matt Dropdown 2: One, Zero, Infinitely Many

Answer 1

Pedro: are the same line, infinitely many

Amy: is

Matt: always, infinitely many

Explanation:

PEDRO: Since the lines are on top of one another, there are infinitely many solutions. These lines are called coinciding lines.

AMY: 3y = 6x + 6 is a multiple of y = 2x + 2. When one equation is a multiple of the other, there are infinitely many solutions to the system.

MATT: When the equation 3y = 6x + 6 is divided by 3, the quotient is equal to the first equation. The equations are equivalent, so they describe the same graphed line.

Answer 2

Pedro Dropdown 1: they Do not Intersect, they Are the same line

Explanation:

3y = 6x + 6

y = 2x + 2

3y-6x = 6... Equation one

y-2x = 2... Equation two

Dividing equation one by 3 gives

Y -2x = 2. Which is same thing with equation 2

So I think the two are same line and do not intersect.