SOLUTION: U is the midpoint of line segment XY. If XY = 16x – 6 and UY = 4x + 9, find the value of x and the measure of XY.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: U is the midpoint of line segment XY. If XY = 16x – 6 and UY = 4x + 9, find the value of x and the measure of XY.      Log On


   

Question 12391: U is the midpoint of line segment XY. If XY = 16x – 6 and UY = 4x + 9, find the value of x and the measure of XY.
Answer by akmb1215(68) About Me  (Show Source):
You can put this solution on YOUR website!
Since U is the midpoint of XY, you know that XY is exactly two times UY. In order to set these equal to one another, multiply UY by two and put it equal to XY. You get the equation: 16x+-+6+=+2%284x%2B9%29. Use the distributive property to begin solving, so you get 16x+-+6+=+8x%2B18. Combine like terms to get 8x+=+24. Then solve for x (x=3).
To find the measure of XY, plug 3 in for x in the formula: 16(3) - 6 = XY. Work it out to get XY = 42.