Systems of Linear Equations Question

Question

Find all the solutions to the following linear system:

y/x + 2x/y = 6/xy

x² + y² = 5

Answer 1

To my knowledge, Linear Algebra is not needed here as this is a typical Systems of Equations problem that is solved via Term Substitution:

(1) Multiply first equation by y and Divide second equation by x: (a.) y^2/x+2x=6/x

(b.) y^2/x+x=5/x

(2) Move terms around to have "y^2/x" by itself in (a.) -> (A.) y^2/x = 6/x - 2x

(3) Substitute (A.) into (b.): (B.) 6/x - 2x + x = 5/x

(4) Solve for x in (B.): -x = -1/x -> x^2 = 1, thus x = 1

(5) Use the known "x" value in equation (b.): 1^2 + y^2 = 5, where y can only be y = 2

Answer; (1,2) as (x,y)