X + y = 8
Xy = 15
Basically solve for one of the 2 variables in either of the functions and plug in the solved variable for the unsolved equation.
X + y = 8
xy = 15
Xy/X = 15/x
y = 15/X
X + y = 8
X + (15/X) = 8.
X/1 + 15/X = 8
Find the common denominator by multiplying by X to both the top and bottom of X/1.
X^2/X + 15/X = 8
(X^2 + 15)/X = 8
X • (X^2 + 15)/X = 8 • X
X^2 + 15 = 8X
X^2 - 8x + 15 = 0
Factor the quadratic
(X-5)(X-3) = 0
X = 5 and X = 3.
Now solve for the y values in each case by substituting the appropriate X value in the equation:
Y = 15/X, so for X = 5
Y = 15/5 = y = 3.
So one solution point would be = (5,3).
Do the same for the other X value.
Y = 15/X, so for X = 3
Y = 15/3 = Y = 5.
The other solution point would be (3,5).
To check if this is the solution to both equations plug in each point for both equations, the equations should be true for each point.
P(5,3) and P(3,5).
