Question

Plug a few points into these 2 equations to prove they only have one solution: 2y=6x+2, y-5x=+2

Answer 1

Let's plug in the points (1,4) and (3,8) into the equations to show that they only have one solution.

For the first equation, when we plug in (1,4):
2y = 6(1) + 2
2y = 8
y = 4

Now when we plug in (3,8):
2y = 6(3) + 2
2y = 20
y = 10

Both of these y values are not the same, so the equations do not have only one solution.

For the second equation, when we plug in (1,4):
y - 5(1) = 2
y - 5 = 2
y = 7

Now when we plug in (3,8):
y - 5(3) = 2
y - 15 = 2
y = 17

Just like the first equation, these y values are not the same, so the equations do not have only one solution.