SOLUTION: Among all pairs of numbers (x,y) such that, 6x+2y=34 find the pair for which the sum of squares , x^2 + y^2 is minimum. Reduce all fractions to the lowest terms. I am stumped h

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Among all pairs of numbers (x,y) such that, 6x+2y=34 find the pair for which the sum of squares , x^2 + y^2 is minimum. Reduce all fractions to the lowest terms. I am stumped h      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 403703: Among all pairs of numbers (x,y) such that, 6x+2y=34 find the pair for which the sum of squares , x^2 + y^2 is minimum. Reduce all fractions to the lowest terms.
I am stumped here I have tried substitution and crossing out and cancellation and the quadradic formula among other variations to solving simple algebra problems and it doesnt seem to matter I cant seem to get the answer right to this type of question I'm very confused.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
remember the equation for a circle (centered at the origin) ___ x^2 + y^2 = r^2

the question is looking for the point on the line, closest to the origin (minimal r^2)

this would be a point on the line, where a perpendicular to the line passes through the origin
___ the equation of this line is ___ 2x - 6y = 0 or 2x = 6y or 6x = 18y

substituting ___ (18y) + 2y = 34 ___ 20y = 34 ___ y = 1.7 (or 17/10)

substituting ___ 2x = 6(1.7) ___ x = 5.1 (or 51/10)