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Which of the following points is the intersection between

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by AAPL » Tue Feb 19, 2019 5:06 am

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Princeton Review

Which of the following points is the intersection between the lines y = 3x + 6 and y = -2x - 4?

A. (2, 0)
B. (0, -2)
C. (-2, 0)
D. (0, 2)
E. (1, 5)

OA C
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by Brent@GMATPrepNow » Tue Feb 19, 2019 5:42 am
AAPL wrote:Princeton Review

Which of the following points is the intersection between the lines y = 3x + 6 and y = -2x - 4?

A. (2, 0)
B. (0, -2)
C. (-2, 0)
D. (0, 2)
E. (1, 5)

OA C
KEY CONCEPT: The point of intersection (call P) of the lines y = 3x + 6 and y = -2x - 4 will be such that the x- and y-coordinates of P will satisfy BOTH equations.

Since both equations are set equal to y, we can write: 3x + 6 = -2x - 4
Add 2x to both sides: 5x + 6 = - 4
Subtract 6 from both sides: 5x = - 10
Solve: x = -2

So, the x-coordinate must be -2
Check the answer choices . . . . . only answer choice C has -2 for the x-coordinate.

Answer: C

ASIDE: We could have also found the y-coordinate by plugging x = -2 into either of the given equations.
For example, take y = 3x + 6 and replace x with -2 to get: y = 3(-2) + 6 = -6 + 6 = 0
So, y-coordinate is 0

Cheers,
Brent
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by [email protected] » Tue Feb 19, 2019 1:19 pm
Hi All,

We're asked which of the following points is the intersection between the lines y = 3x + 6 and y = -2x - 4. This question can be solved in a number of different ways, including by TESTing THE ANSWERS.

Since we're dealing with two lines - and we now that the two lines intersect - there will only be one co-ordinate that 'fits' both equations. Looking at the answer choices, the numbers involved are all fairly simple, so we just have to 'plug in' each pair until we find the one that properly fits both of the given lines.

Since X=0 is in two of the answers, we can start there. Plugging in X=0 will get us DIFFERENT values for Y though (y = +6 and Y = -4), so neither of those answers is correct and we can eliminate Answers B and D. Answer A gives us (2,0) which does not fit the first equation. Answer C DOES match both equations though, so it must be the answer.

Final Answer: C

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Rich
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by Scott@TargetTestPrep » Thu Feb 21, 2019 4:52 pm
AAPL wrote:Princeton Review

Which of the following points is the intersection between the lines y = 3x + 6 and y = -2x - 4?

A. (2, 0)
B. (0, -2)
C. (-2, 0)
D. (0, 2)
E. (1, 5)

OA C
To find the point of intersection of two lines, we set their equations equal to each other:

3x + 6 = -2x - 4

5x = -10

x = -2

Substituting the x-value = -2 into either equation, we obtain y = 0, and thus (-2, 0) is the point of intersection.

Answer: C

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