MATH SOLVE

4 months ago

Q:
# Solve for x and y:3/x -1/y =13/101/x + 2/y =9/10

Accepted Solution

A:

Answer: (x, y) = (2, 5)Step-by-step explanation:I find it easier to solve equations like this by solving for x' = 1/x and y' = 1/y. The equations then become ... 3x' -y' = 13/10 x' +2y' = 9/10Adding twice the first equation to the second, we get ... 2(3x' -y') +(x' +2y') = 2(13/10) +(9/10) 7x' = 35/10 . . . . . . simplify x' = 5/10 = 1/2 . . . . divide by 7Using the first equation to find y', we have ... y' = 3x' -13/10 = 3(5/10) -13/10 = 2/10 = 1/5So, the solution is ... x = 1/x' = 1/(1/2) = 2 y = 1/y' = 1/(1/5) = 5 (x, y) = (2, 5)_____The attached graph shows the original equations. There are two points of intersection of the curves, one at (0, 0). Of course, both equations are undefined at that point, so each graph will have a "hole" there.