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Which of the following points is the intersection between

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by Brent@GMATPrepNow » Fri Sep 07, 2018 5:19 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

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Which of the following points is the intersection between

by fskilnik@GMATH » Fri Sep 07, 2018 1:24 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)
\[\left\{ {\begin{array}{*{20}{c}}
{y = 3x + 6} \\
{y = - 2x - 4}
\end{array}\,\,\,\,\,\begin{array}{*{20}{c}}
{\left( 1 \right)} \\
{\left( 2 \right)}
\end{array}} \right.\,\,\,\,\,\, \sim \,\,\,\,\left\{ {\,\begin{array}{*{20}{c}}
{y = 3x + 6} \\
{0 = 5x + 10}
\end{array}\,\,\,\,\,\begin{array}{*{20}{c}}
{\left( 1 \right)} \\
{\left( {\left( 1 \right) - \left( 2 \right)} \right)}
\end{array}} \right.\,\,\,\,\,\,\, \sim \,\,\,\,\left\{ \begin{gathered}
\,y = 3 \cdot \left( { - 2} \right) + 6 = 0 \hfill \\
\,x = - 2 \hfill \\
\end{gathered} \right.\]
This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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by Scott@TargetTestPrep » Sat Sep 29, 2018 5:05 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)
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

Since (-2, 0) is the only ordered pair with x-value = -2, then (-2, 0) must be the point of intersection.

Answer: C

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by [email protected] » Sun Sep 30, 2018 3:48 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. Sometimes, the fastest way to answer a question is to use 'brute force'; the five answers are co-ordinates and we know that one of them will 'fit' both equations, so we just have to do enough work to prove which one fits (and that one will be the correct answer.

Answer A. (2, 0) --> fits the first equation, does NOT fit the second equation
Answer B. (0, -2) -->does NOT fit either equation
Answer C. (-2,0) --> fits BOTH equations

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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