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At what point do the two lines intersect

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At what point do the two lines intersect

by Brent@GMATPrepNow » Thu Jan 15, 2009 4:31 pm
In the coordinate plane, line A is defined by the equation 3x+2y=k, and line B is defined by the equation jx-y=-7. At what point do the two lines intersect?
(1) Line A passes through the point (0,7)
(2) Line B passes through the point (3,1)
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Re: At what point do the two lines intersect

by logitech » Thu Jan 15, 2009 5:00 pm
I will not let you to ruin my night Brent! :)

(1) Line A passes through the point (0,7)

If we use this point in second equation we will see that it will satisfy the second equation as well so (0,7) is where they meet! :)


(2) Line B passes through the point (3,1)

We can find that the second equation is y=-2x+7

We don't know anything about K in the first equation, so I would choose A

COME ON! A!! COME ON!!!!!! :)
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by Brent@GMATPrepNow » Thu Jan 15, 2009 5:09 pm
Nice work, Logitech - A it is :)

Here's my solution, which I prepared earlier:
One strategy is to rewrite both equations in slope y-intercept form to get a better idea of how the variables k and j affect the lines.
We get line A: y = -3/2 x + k/2 (here we see that the slope of line A is -3/2, and k affects the line’s y-intercept)
We also get line B: y = jx + 7 (here we see that j affects the slope of the line, and the y-intercept is 7

(1) This tells us that the y-intercept of line A is 7. Hey, the y-intercept of line B is also 7, so the two lines must intersect at (0,7) (SUFFICIENT)
(2) This information will help us to determine the value of j and fully define the equation of line B. However, this information tells us nothing about line A. All we know about line A is that it has slope of -3/2. Since we don’t know the y-intercept of line A, we have no idea where line A is located on the coordinate plane. If we can’t fix line A’s position in the coordinate plane, we can’t determine its intersection with line B (INSUFFICIENT)

The correct answer is A
Last edited by Brent@GMATPrepNow on Fri Jan 16, 2009 6:35 am, edited 1 time in total.
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by 4meonly » Fri Jan 16, 2009 12:31 am
We can find that the second equation is y=-2x+7

y=jx+7
if y=3 and x=1 => 3 = j*1 + 7 => -4=j*1 => j=-4
we have y=-4x+7
However, this will not affect the answer A. :D
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by logitech » Fri Jan 16, 2009 12:47 am
4meonly wrote:
We can find that the second equation is y=-2x+7

y=jx+7
if y=3 and x=1 => 3 = j*1 + 7 => -4=j*1 => j=-4
we have y=-4x+7
However, this will not affect the answer A. :D
(3,1) means X = 3 and Y=1

Big Brother is watching you! B-)
LGTCH
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