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What is the point of intersection of the lines 3x + 2y = 16 and 6x + 4y = 24?

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What is the point of intersection of the lines 3x + 2y = 16 and 6x + 4y = 24?

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justaguide's profile pic

Posted (Answer #1)

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The point of intersection of the lines 3x + 2y = 16 and 6x + 4y = 24 has to be determined.

Looking at the two equations it can be seen that the slope of the line 3x + 2y = 16 is -3/2 and the slope of the line 6x + 4y = 24 is also -6/4 = -3/2. As the two line are parallel to each other they do not intersect each other.

The two lines 3x + 2y = 16 and 6x + 4y = 24 do not intersect each other.

Wilson2014's profile pic

Posted (Answer #2)

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3x+2y=16

It is indeed true that the two lines do not intersect due to them having the same slope and not being the same line. If they are not the same line and have the same slope, that means that they are parallel to each other. To be able to come to this conclusion, one must find the slope. To find the slope in this problem, convert the equation to slope-intercept form, which is y=mx+b, where m=slope and b=y-intercept.

`3x+2y=16`

`=> 2y=-3x+16`

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

Therefore, the slope for this line is -3/2. The same method can be applied on the other line equation and we would see that the slope of that line is also -3/2; thus, they are parallel lines since they don't have the same y-intercept to indicate them being the same lines. 

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