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I think there must be a typo in line 2 definition. Line should be represented as equation. y2-4x+6 shoul be equal to something, in the way it's represented it doesn't make any sense for me. Let's find out which kind of typo there is:

y2-4x+6?

1. y1=5x-3, y2=4x+6 (meaning that - sign should be =): 5x-3=4x+6 --> x=9, y=42 --> intersect at point (9,42), no such answer choice.

2. y1=5x-3, y2-4x+6=0 (meaning that LHS equals to 0): 5x-3=4x-6 --> x=-3, y=-18 --> intersect at point (-3,-18), no such answer choice.

3. y1=5x-3, y2=-4x+6 (meaning that = sign is just missing) 5x-3=-4x+6 --> x=1, y=2 --> intersect at point (1,2), answer choice D.

So, I suppose the third option detects the typo. But it would be easier if we knew the OA to say with certainty.
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I think there must be a typo in line 2 definition. Line should be represented as equation. y2-4x+6 shoul be equal to something, in the way it's represented it doesn't make any sense for me. Let's find out which kind of typo there is:

y2-4x+6?

1. y1=5x-3, y2=4x+6 (meaning that - sign should be =): 5x-3=4x+6 --> x=9, y=42 --> intersect at point (9,42), no such answer choice.

2. y1=5x-3, y2-4x+6=0 (meaning that LHS equals to 0): 5x-3=4x-6 --> x=-3, y=-18 --> intersect at point (-3,-18), no such answer choice.

3. y1=5x-3, y2=-4x+6 (meaning that = sign is just missing) 5x-3=-4x+6 --> x=1, y=2 --> intersect at point (1,2), answer choice D.

So, I suppose the third option detects the typo. But it would be easier if we knew the OA to say with certainty.

yes, there was a typo in the first image equal sign was missing... thnx for pointing that out. You got this nailed.

Since at the point of intersection, the two equations will have the same values of x and y, we set the two equations equal to each other. This gives an equation that we can solve for x We substitute that x value in one of the line equations (it doesn't matter which) and solve it for y.

y1 = 5x - 3 y2 = -4x+6

At intersection point, y1 = y2 5x - 3 = -4x + 6 x = 1

By substituting value of x in any of the above 2 equations we get y = 5*1 - 3 y = 2

Re: At which point do the lines y1 = 5x - 3 and y2 = -4x + 6 [#permalink]

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01 May 2015, 07:16

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In these types of questions, since the answer choices ARE co-ordinates, we just need to find the one co-ordinate that "fits" both equations.

Y = 5X - 3 and Y = -4X + 6

Answer A: (1/3, 14/3) - does NOT fit the first equation. Answer B: (1/3, 22/3) - does NOT fit the first or second equation. Answer C: (1, -2) - does NOT fit the first or second equation Answer D: (1, 2) - Fits BOTH equations Answer E: (3, -6) - no need to check this one (but it does NOT fit the first equation.

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