Find points intersection curve xy=6 line y=9-3x

Answer 1

To answer this question, solve the two equations simultaneously. The easiest way to do this is with substitution. Use the information from the second equation, y = 9-3x, and replace y with 9-3x in the first equation.

xy = 6

x(9-3x) = 6

Distribute:

9x - 3x² = 6

Write in standard form:

-3x² + 9x - 6 = 0

Divide by -3:

x² - 3x + 2 = 0

Factor:

(x - 2)(x - 1) = 0

Solve:

x - 2 = 0 means that x = 2

x - 1 = 0 means that x = 1

If x = 2, then using xy=6 :

2y=6

y = 3

If x = 1, then using xy=6,

1y=6

y=6

One point of intersection is (2, 3) and another point is (1, 6)