Question 27708
x^2-y^2=9
x^2+9y^2=169



This set of equations can be solved by elimination and sustitution.  First, multiply the first equation by -1, and then add the two equations together.  This will eliminate x and allow us to solve for y.


-x^2+y^2=-9
x^2+9y^2=169
____________
10y^2=160
y^2=16
y=4


Now that you have the value of y you can substitute it in any one of the two equations and solve for x.
Let's use the first equation.

x^2-y^2=9
x^2-(4)^2=9
x^2-16=9
x^2=25
x=5


I hope that you were able to follow the solution.  To check our answer substitute x=5 and y=4 in the equations.