[x+ay=b],[ax-by=c]

Solve the following system of equations by method of cross-multiplication: x+ay=b,quad ax-by=c

Let a,b,c be real numbers with a^2 + b^2 + c^2 =1. Show that the equation |[ax-by-c,bx+ay,cx+a],[bx+ay,-ax+by-c,cy+b],[cx+a,cy+b,-ax-by+c]|=0 represents a straight line.

Let a,b,c be real numbers with a^2 + b^2 + c^2 =1 . Show that the equation |[ax-by-c,bx+ay,cx+a],[bx+ay,-ax+by-c,cy+b],[cx+a,cy+b,-ax-by+c]|=0 represents a straight line.

Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],[cx+az,ay+bz,cz-ax-by]| = (a^2+b^2+c^2)(ax+by+cz)(x^2+y^2+z^2)

Solve the following system of equations: ax+by=c, x+ay=1+c

"Solve for x and y; ax+by=a-b, "bx-ay=a+b

Find the value of x and y: ax +by =a-b bx-ay =a+b

Solve by the method of cross multiplication: ax+by=a-b, bx-ay=a+b