Question

Solve 5x + 4/y =7 and 4x + x/y =5 simultaneously.​

Answer 1

9514 1404 393

Answer:

  (x, y) ≈ (1.1642, 3.3930) and (3.4358, -0.39297)

Step-by-step explanation:

Solve the first equation for y, then substitute into the second.

  5x +4/y = 7

  4/y = 7 -5x

  4/(7 -5x) = y

Then the second equation becomes ...

  4x +x/(4/(7 -5x)) = 5

  4x +x(7 -5x)/4 = 5

  16x +7x -5x^2 = 20 . . . . . multiply by 4

  5x^2 -23x +20 = 0 . . . . . put in standard form

We can use the quadratic formula to solve this.

  x = (23±√((-23)² -4(5)(20)))/(2(5)) = (23±√129)/10

  x = 2.3 ±√1.29 ≈ {1.1642, 3.4358}

  y = 4/(7 -5x) = {3.3930, -0.39297}

Solutions are (x, y) ≈ (1.1642, 3.3930) and (3.4358, -0.39297).