If `5b=6a+16 and 9b=7b-20`, then what is the value of `3a-2b`?

Options

A. `-8`
B. `-4`
C. `4`
D. `8`

Answer

B

Explanation

Difficult: Easy
Category: Heart of Algebra/ System of Linear Equations
Strategic Advice: Whenever you're asked for an unusual quantity, rather than just the value of one variable or the other, there's good chance that a time-saving shortcut (like simply adding or subtracting the equations) exists.
Getting to the Answer: Start by rewriting the equations, so that they are in the same form. After doing so, if you look closely at the coefficient, you'll see that adding the two equations will yield exactly what you're asked to find:
`5b=6a+16 to -6a+5b=16`
`{:(5b=6a+16 to -6a+5b=16),(9a=7b-20to ul(9a-7b=-20)),(" "3a-2b=-4):}`
The sum of the two equations tells you that `3a-2b` is `-4`, making (B) is correct answer.