Question

Which ordered pair is the best estimate of the solution of the system 3x+y=4 x-3y=4?

Answer 1

$3x+y=4\ \ \ \ \ \ ..............equation(1)\\x-3y=4\ \ \ \ \ \ ..............equation(2)\\\\ Using~equation~(2), \\\\ x-3y=4\\x=4+3y\\\\Now,\ using\ the\ value\ of\ x\ in\ equation\ (1),\ we\ get,\\\\(4+3y)-3y=4\\\\4=4$

Since all the variables cancel out and the coefficient equal to eachother, this system of equation has infinitely many solutions!