Using Cramer's rule to solve a system?

Question

i need some help solving this system using cramer's rule

xcosø - ysinø = 1
xsinø - ycosø = 1

for the unknowns x and y as a function of ø.

find (x^2) + (y^2) and show that the solution point (x,y) is always a constand distance from the origin.

all help is greatly appreciated.

Answer 1

Solving the equations by Cramer's rule gives you, x=1/(cos phi+sin phi) and y=-1/(cos phi +sin phi)
Substitute above values of x and y in x^2 +y^2.
That should give you 1 as the constant distance.
Since cos^2 theta +sin^2 theta=1 for any theta, solution point (x,y) will always be at a constant distance from origin.
x^2 +y^2=a^2(here a=1) is the equation of the standard circle with centre at origin O(0,0) and radius a.