If the system of equations 6x−4y=a,6y−9x=b.has a solution (x,y) where x and y are both nonzero, find ab, assuming b is nonzero.
6x - 4y = a → 6x - 4y = a → 6x - 4y = a
6y - 9x = b → -9x + 6y = b → 6x - 4y = (-2/3)b
The determinant of the coefficient matrix = 0
If a = (-2/3)b, we have infinite solutions where x, y are both non-zero
So... we have infinite solutions when a/b = -2/3
