Question

solve the system xy^3=10^14 x^2/y=10^7

Answer 1

Solve one equation for a certain variable (in this case I'd be inclined to solve the first one for x), plug that value of x into your second equation, and solve for y. Then, with that value of y, substitute it into any of your equations, and you'll get your value of x.

Answer 2

y=x^2/10^7
put in eq 1
x(x^2/10^7)^3=10^14
x^7=10^14*10^21=10^35=(10^5)^7
x=10^5
y=10^3