Question

Select the system of equations that corresponds to the given graph.

graph of two lines. Both lines have a negative slope and go through the points 2 comma 0 and 0 comma 4

4x + y = 6
6x + 3y = 6

−3x + y = 2
4x + 2y = 4

2x + y = 4
6x + 3y = 12

4x + 2y = 6
6x + 3y = 12

Answer 1

there is only one system where both lines go through the point (0, 4):

2x+y=4
6x+3y=12

notice that if you solve either line for y (to get into slope intercept form) you get the same line (if the lines share two points, then they are the same line)

2x+y=4
y=-2x+4

also

6x+3y=12
3y=-6x+12
y=-2x+4

the third system is the answer

Answer 2

@mandolino i had this same question, I chose the third system and i got it wrong :(