I've got a few questions that IbelieveI solved correctly but wanted to check on. I have graphed them and they seem to check out....

The questions, and my working for them, are as follows:

1: 3x+y=5

-2+3y=4

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3x+y=5 ->

3x+y-3x=5-3x ->

y=5-3x therefore

if: x=0 y=5

x=1 y=2

x=2 y=(-1)

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-2x+3y=4 ->

-2x+3y-(-2x)=4-(-2x) ->

3y=4+2x ->

y = 4/3 + (2/3)x therefore

if: x = 0 y = 1 1/3

x = 1 y = 2

x = 2 y = 2 2/3

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answer is: x = 1 y = 2, the lines intersect.

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2: 2x = y + 1

2x - y = 5

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2x = y + 1 ->

y = 2x - 1 therefore

if: x = 0 y = (-1)

x = 1 y = 1

x = 2 y = 3

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2x - y = 5 ->

2x - y + 2x = 5 + 2x ->

y = 5 + 2x therefore

if: x = 0 y = 5

x = 1 y = 7

x = 2 y = 9

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answer is: none, the lines are parallel

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3: 3x + 2y = 8

6x + 4y = 16

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3x + 2y = 8 ->

3x + 2y - 3x = 8 - 3x ->

2y = 8 - 3x ->

y = 4 - (3/2)x therefore

If: x=0 y=4

x=1 y=2 1/2

x=2 y=1

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6x+4y=16 ->

6x+4y-6x=16-6x ->

4y=16-6x ->

y=4-(3/2)x therefore

If: x=0 y=4

x=1 y=2 1/2

x=2 y=1

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answer: infinite, the lines coincide

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Thanks!