SOLUTION: In rectangle ABCD, diagonals AC and BD intersect at E. If AE= 3x+y, BE= 4x-2y, and CE= 20, find x and y. Please help thank you!

Algebra ->  Rectangles -> SOLUTION: In rectangle ABCD, diagonals AC and BD intersect at E. If AE= 3x+y, BE= 4x-2y, and CE= 20, find x and y. Please help thank you!      Log On


   



Question 1008264: In rectangle ABCD, diagonals AC and BD intersect at E. If AE= 3x+y, BE= 4x-2y, and CE= 20, find x and y.

Please help thank you!

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

In rectangle ABCD, diagonals AC and BD intersect at E.

If AE=+3x%2By, BE=+4x-2y, and CE=+20,
find x and y:
since you have a rectangle, diagonals AC and BD are same length
thenAE=+CE and BE=+CE
so, we have
+3x%2By=20....eq.1
+4x-2y=20....eq.2
----------------------...both sides of eq.1 multiply by 2


+6x%2B2y=40....eq.1
+4x-2y=20....eq.2
----------------------........add both eq.1 and eq.2
+6x%2Bcross%282y%29%2B4x-cross%282y%29=40%2B20
+10x=60
+x=60%2F10
+highlight%28x=6%29
now find y
+3x%2By=20....eq.1
+y=20-3x
+y=20-3%2A6
+y=20-18
highlight%28+y=2%29