If x = 2t and y = t/3 what is the value

John Robertson

x=2t, y=t/3, x^2-y^2=?

Prompt: quick survey of 1) and 2) show info is given in "t," and I can convert x^2-y^2 into "t" based off what is given, so I did so:
-> x^2-y^2 = (2t)^2 - (t/3)^2 = 4t^2 - (t^2)/9
-> Also, difference of two squares here, so 4t^2 - (t^2)/9 = (2t+t/3)(2t-t/3). Might not be useful but sometimes common factoring shortcuts like that seem to expose answers down the line
->QED: to solve x^2 - y^2= ?, you can do so by solving for t

1) t^2-3=6. Looks like I can solve for t, but solved out a bit just in case
-> t^2=9, t=+/- 3, prompt is solvable, (S)

2) t^3= -27, t= -3, prompt is solvable (S)

Answer: D, both independently sufficient,

Feb 17, 2017 • Comment