If 6x - 15y = 33, and 6y - x = -18, what is the sum

Answer A
6x - 15y = 33
6y - x = -18

- x + 6y = -18 ( multiply it by 6 )
-6x + 36y = -108

+ 6x - 15y = +33,
- 6x + 36y = -108

21y = -75
Y = -25/7

Putting value of Y

x = 6y + 18
x = 6*-25/7 + 18
x = -150/7 + 18
x = -150 + 126/7
x = -24/7

Sum of x+y = -24 - 25/7
x+y = -49/7
x+y = -7

We're given the following system of equations:
6x - 15y = 33
6y - x = -18

OBSERVATION #1: In the top equation, all three terms (6x, 15y and 33) are divisible by 3.
So, we can create a simpler, yet equivalent, equation by dividing both sides by 3 to get:
2x - 5y = 11
6y - x = -18

OBSERVATION #2: The x and y terms of the two equations are arranged differently.
So let's rewrite the bottom equation as follows:
2x - 5y = 11
-x + 6y = -18

OBSERVATION #3: The question is NOT asking us to determine the individual values of x and y; it's asking us to find the SUM of x and y (i.e., x + y)

Important: When it comes to solving systems of equations like this, there are two possible approaches:
i) The substitution method, where you solve one equation for a particular variable, and then substitute that into the other equation and solve.
ii) The elimination method, where you can either add or subtract equations to eliminate a variable.
In most cases, the elimination method is faster, so be sure to know it.

Notice that, if we take the following system...
2x - 5y = 11
-x + 6y = -18
... and ADD the two equations we get: x + y = -7

Answer: A

If you're up for it, here's another question involving a system of equations: https://gmatclub.com/forum/if-6x-7y-11- ... 30816.html

Cheers,
Brent

6X - 15Y = 33
= 2X - 5y = 11 - (1)

6Y - X = -18 - (2)

(1) + (2)

= 2X - X -5y +6y = 11- 18
= X + Y = -7

OA A!

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