SOLUTION: 4x-y=7 and xy=15 y=15/x 4x-(15/x)=7 multiply everything by x and get 4x^-7x-15=0 when you factor x=-5/4 and x=3

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Question 1057021: 4x-y=7 and xy=15 y=15/x 4x-(15/x)=7 multiply everything by x and get 4x^-7x-15=0 when you factor x=-5/4 and x=3
Found 3 solutions by ikleyn, MathTherapy, jenny.rice:
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.
4x - y = 7,   (1)
xy = 15.      (2)

From (1), express y = 4x-7 and substitute it into equation (2), replacing y. You will get a single quadratic equation

x*(4x-7) = 15.

Simplify:

4x^2 - 7x - 15 = 0,

x%5B1%2C2%5D = %287+%2B-+sqrt%287%5E2+-+4%2A4%2A%28-15%29%29%29%2F%282%2A4%29 = %287+%2B-+sqrt%28289%29%29%2F8%29 = %287+%2B-+17%29%2F8.

x%5B1%5D = 24%2F8 = 3  --->  y = 15%2Fx = 15%2F3 = 5.

x%5B2%5D = -10%2F8 = -5%2F4 = -1.25.  --->  y = 15%2Fx = 15%2F%28%28-5%2F4%29%29 = -12.

Answer.  There are two solutions:  (x,y) = (3,5)  and  (x,y) = (-1.25,-12).

For many other similar solved problems see the lesson
    - Solving systems of algebraic equations of degree 2 and degree 1
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of equations that are not linear".


Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

4x-y=7 and xy=15

Answer by jenny.rice(1) About Me  (Show Source):
You can put this solution on YOUR website!
4x-y=7 and xy=15 y=15/x 4x-(15/x)=7 multiply everything by x and get 4x^-7x-15=0 when you factor x=-5/4 and x=3