1. Determine if two lines are parallel `5x+2y-11=0` and `15x+6y-11=0`

Solution:
When two lines are parallel, their slopes are equal.

1. Slope of line `5x+2y-11=0`

`5x+2y-11=0`

`:. 2y=-5x+11`

`:. y=-(5x)/(2)+11/2`

`:.` Slope `m_1=-5/2`


2. Slope of line `15x+6y-11=0`

`15x+6y-11=0`

`:. 6y=-15x+11`

`:. y=-(5x)/(2)+11/6`

`:.` Slope `m_2=-5/2`

Here `m_1=m_2`, so these two lines are parallel

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2. Determine if two lines are parallel `x-2y+15=0` and `2x-4y-4=0`

Solution:
When two lines are parallel, their slopes are equal.

1. Slope of line `x-2y+15=0`

`x-2y+15=0`

`:. 2y=x+15`

`:. y=(x)/(2)+15/2`

`:.` Slope `m_1=1/2`


2. Slope of line `2x-4y-4=0`

`2x-4y-4=0`

`:. 4y=2x-4`

`:. y=(x)/(2)-1`

`:.` Slope `m_2=1/2`

Here `m_1=m_2`, so these two lines are parallel

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3. Determine if two lines are parallel `x-y=1` and `2x-3y+1=0`

Solution:
When two lines are parallel, their slopes are equal.

1. Slope of line `x-y=1`

`x-y=1`

`:. y=x-1`

`:.` Slope `m_1=1`


2. Slope of line `2x-3y+1=0`

`2x-3y+1=0`

`:. 3y=2x+1`

`:. y=(2x)/(3)+1/3`

`:.` Slope `m_2=2/3`

Here `m_1!=m_2`, so these two lines are not parallel

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4. Determine if two lines are parallel `x-2y+15=0` and `3x+y-4=0`

Solution:
When two lines are parallel, their slopes are equal.

1. Slope of line `x-2y+15=0`

`x-2y+15=0`

`:. 2y=x+15`

`:. y=(x)/(2)+15/2`

`:.` Slope `m_1=1/2`


2. Slope of line `3x+y-4=0`

`3x+y-4=0`

`:. y=-3x+4`

`:.` Slope `m_2=-3`

Here `m_1!=m_2`, so these two lines are not parallel

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