Solve this problem

Question

Answer 1

8x - y = -6

xy = 9

This system is a straight line intersecting a hyperbola.

Use substitution method.

y = 9/x

8x - 9/x = -6 Mult both sides by x to eliminate fraction

8x² - 9 = -6x Re-write as a quadratic equation

8x² + 6x - 9 = 0 Use a•c method to factor by grouping. (a•c = -72; best factors will be -6 and 12)

8x² +12x - 6x - 9 = 0; 4x(2x + 3) - 3(2x + 3) = 0

(4x - 3)(2x + 3) = 0

4x - 3 = 0; 4x = 3; x = 3/4. Then y = 9(4/3) = 12 Solution at (3/4, 12)

2x + 3 = 0; 2x = -3; x = -3/2 Then y = 9(-2/3) = -6 Solution at (-3/2,-6)

Suggest graph on Desmos Graphing Calculator website to visualize.