Line K is defined by the equation 3x - 4y = 7, and line L is defined by

BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:39 am

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

Answer: C
Source: GMAT prep now

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

Since our goal is to determine the value of m+n, we need to find an m-value and an n-value such that 3m - 4n = 7 AND 2m + 2n = -5

Alternatively, if we recognize that, in order to find the sum m+n, then we don't actually need to know the individual values of m and n.
This means we can avoid solving this system of equations by recognizing that the desired sum (m + n) is "hiding" in the second equation.
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