At which point do the lines y1 = 5x - 3 and y2 = -4x + 6

Question

At which point do the lines y1 = 5x - 3 and y2 = -4x + 6 intersect?

A. (1/3, 14/3)
B. (1/3, 22/3)
C. (1, -2)
D. (1, 2)
E. (3, -6)

Bunuel · Answer

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.

Bunuel · Answer

I see the image is corrected know, so option 3 with answer D is correct.

gmattokyo · Answer

yes, there was a typo in the first image

equal sign was missing... thnx for pointing that out. You got this nailed.

manjusu · Answer

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

therefore D is the answer (1,2)

Cheers,
Suman

madn800 · Answer

solving the two equations

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

-____+__-__
0 =9x-9
9x =9
x=1
Now take any one of the above equations and substitute x=1 in it
we get y=2
so answer is (1,2)

Lobro · Answer

to find intersect, y would be the same for both functions

so solve

5x - 3 = -4x +6 ---> 9x = 9 ---> x = 1

fill in 1 in ether of the two given function to return y = 2

intersect is at (1,2)

answer D is correct

EMPOWERgmatRichC · Answer

Hi All,

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.

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

At which point do the lines y1 = 5x - 3 and y2 = -4x + 6

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

At which point do the lines y1 = 5x - 3 and y2 = -4x + 6

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards