Answer:
Step-by-step explanation:
xy = 300
x + y = 50 Solve for y
y = 50 - x substitute into xy = 300
x(50 - x) = 300 Remove the brackets.
50x - x^2 = 300 Bring the left to the right.
0 = x^2 - 50x + 300
This is a quadratic. It will have 2 solutions.
a=1
b = - 50
c = 300
Put these into the quadratic equation.
It turns out that x has two values -- both plus
x1 = 42.03
x2 = 6.97
x1 + y1 = 50
42.03 + y = 50
y = 50 - 42.03
y = 7,97
(42.03 , 7.97)
====================
x2 + y2 = 50
6.97 + y2 = 50
y2 = 50 - 6.97
y2 = 43.03
(6.97 , 43.03)
Answer:
x ≈ 6.97, y ≈ 43.03; x ≈ 43.03, y ≈ 6.97
Step-by-step explanation:
System: x + y = 50, xy = 300
Alter 1st equation: y = 50 - x
Substitute: x(50 - x) = 300
Distribute: -x² + 50x = 300
Subtract: -x² + 50x - 300 = 0
Quadratic formula: x = (-50 ± √(2500 - 4 * -1 * -300))/(-2)
Simplify: x = (-50 ± √1300)/-2
Distribute: x = 25 ± (10√13)/-2
Simplify: x = 25 - 5√13 --> x ≈ 6.97, x = 25 + 5√13 --> x ≈ 43.03
Substitute: 6.97 + y = 50 --> y ≈ 43.03, 43.04 + y = 50 --> y ≈ 6.97
