X + k y = 1 k x + y = 1 / * ( - k ) ---------------- x + k y = 1 - k² x - k y = - k -------------------- x - k² x = 1 - k x ( 1 - k² ) = 1 - k x = ( 1 - k ) / ( 1 - k² ) = ( 1 - k ) / ( 1 - k ) ( 1 + k ) y = 1 - k( 1 - k )/( 1 - k² ) y = ( 1 - k ) / ( 1 - k² ) = ( 1 - k ) / ( 1 - k ) ( 1 + k ) a ) For k = - 1 this system has no solution. b ) For k ≠ - 1 and k ≠ 1, the system has unique solution: ( x , y ) = ( 1/ (1 + k) , 1/( 1 + k ) ). c ) For k = 1, there are infinitely many solutions.
Answer: 35 more times How: (if she gets 60 points for each grocery store visit then first do 2580-480=2100. she still needs 2100 points so then 2100/60 = 35 grocery visits!)
