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Joined: 10 Apr 2015
Posts: 6218
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Line K is defined by the equation 3x - 4y = 7, and line L is defined
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02 Mar 2022, 16:25
02 Mar 2022, 16:25
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Line K is defined by the equation 3x - 4y = 7, and line L is defined by the equation 2x + 2y = -5. If the point (m, n) is the intersection of lines K and L, what is the value of m + n?
A) -7
B) -3
C) -2.5
D) -3/7
E) -2
A) -7
B) -3
C) -2.5
D) -3/7
E) -2
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: Line K is defined by the equation 3x - 4y = 7, and line L is defined
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08 Mar 2022, 05:25
08 Mar 2022, 05:25
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Expert Reply
The point of intersection is found by solving the 2 equations
3m - 4n = 7
2m + 2n = -5
Multiplying equation (2) by 2 and adding, we get 3m - 4n + 2(2m + 2n) = 7 + 2(-5)
3m - 4n + 4m + 4n = -3
7m = -3
m = -3/7
Putting m = -3/7 in equation (2), we get 2*(-3/7) + 2n = -5
2n = -5 + 6/7 = -29/7
n = -29/14
Therefore m + n = -3/7 + (-29/14) = (-6 - 29) / 14 = -35/14 = -5/2 = -2.5
Option C
3m - 4n = 7
2m + 2n = -5
Multiplying equation (2) by 2 and adding, we get 3m - 4n + 2(2m + 2n) = 7 + 2(-5)
3m - 4n + 4m + 4n = -3
7m = -3
m = -3/7
Putting m = -3/7 in equation (2), we get 2*(-3/7) + 2n = -5
2n = -5 + 6/7 = -29/7
n = -29/14
Therefore m + n = -3/7 + (-29/14) = (-6 - 29) / 14 = -35/14 = -5/2 = -2.5
Option C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Line K is defined by the equation 3x - 4y = 7, and line L is defined
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08 Mar 2022, 09:57
08 Mar 2022, 09:57
1
GreenlightTestPrep wrote:
Line K is defined by the equation 3x - 4y = 7, and line L is defined by the equation 2x + 2y = -5. If the point (m, n) is the intersection of lines K and L, what is the value of m + n?
A) -7
B) -3
C) -2.5
D) -3/7
E) -2
A) -7
B) -3
C) -2.5
D) -3/7
E) -2
Key concept: the coordinates of each point on a line are solutions to the equation of that line.
So, if the point (m, n) is the intersection of lines K and L, then the coordinates x = m and y = n must be solutions to BOTH equations.
So, we can write: 3m - 4n = 7 AND 2m + 2n = -5
To determine the value of m+n, we COULD solve the system of equations for the individual values of m and n, and then calculate the value of the sum m + n.
HOWEVER, here's a much faster solution....
Recognize that, in order to find the sum m+n, we don't actually need to know the individual values of m and n.
Also recognize that the desired sum (m + n) is "hiding" in the equation 2m + 2n = -5 .
That is, we can take 2m + 2n = -5, and divide both sides by 2 to get the EQUIVALENT equation m + n = -2.5
Answer: C
Cheers,
Brent
