SOLUTION: Find the values of x and y. In equangular triangle ABC, AB = 4x - y, BC = 2x + 3y, and AC = 7.

Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: Find the values of x and y. In equangular triangle ABC, AB = 4x - y, BC = 2x + 3y, and AC = 7.      Log On

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Question 170618This question is from textbook Geometry
: Find the values of x and y.
In equangular triangle ABC, AB = 4x - y, BC = 2x + 3y, and AC = 7.This question is from textbook Geometry

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
AB,BC,and AC are all equal to each other because this is an equilateral triangle....with this info we can create 2 equations with 2 unknowns(a set of linear equations)
:
4x-y=7...eq 1
2x+3y=7..eq 2
:
multiply eq 1 by 3 and add to eq 2 to eliminate the y terms
:
12x+2x=21+7
:
14x=28
:
highlight%28x=2%29
plugging x's value into eq 1 we get 4(2)-y=7......solving for y
:
highlight%28y=1%29