Question
Plug a few points into these 2 equations to prove they only have one solution: 2y=6x+2, y-5x=+2
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GPT 3.5
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.
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.
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