Question

X2 + xy=15; y2 + xy=10​

Answer 1

To solve this system of equations, we can use the method of substitution.

From the first equation, we can solve for x in terms of y:

x = (15 - xy)/y

Then, we can substitute this expression for x into the second equation:

y^2 + (15 - xy)/y * y = 10

Simplifying:

y^2 + 15 - xy = 10

y^2 - xy + 5 = 0

Now we can solve for y using the quadratic formula:

y = [-(-x) ± sqrt((-x)^2 - 4(1)(5))]/(2*1)

y = [x ± sqrt(x^2 - 20)]/2

Substituting this expression for y back into the equation we obtained for x earlier:

x = (15 - x[y ± sqrt(x^2 - 20)])/[y(2)]

Simplifying:

2xy ± xsqrt(x^2 - 20) = 15 - 2x

xsqrt(x^2 - 20) = 15 - 2xy - 2x

x^2(x^2 - 20) = (15 - 2xy - 2x)^2

Expanding and simplifying:

x^4 - 20x^2 - 4x^3y + 60x - 4xy^2 - 225 = 0

This is a quartic equation in x. Solving it exactly would be quite involved, so we will stop here. However, we can use numerical methods or approximations to find numerical solutions for x and y.