The number of ordered pairs (x, y) satisfying the system of equations x + y = 1 x + y = 3 where x, y [0, 6 ] , is _______.

Step-by-step solution

Given the system of equations: x + y = 1 ... (i) x + y = 3 ... (ii) Squaring both equations and adding them: ( x + y)^2 + ( x + y)^2 = 1^2 + ( 3 )^2 ( ^2 x + ^2 x) + ( ^2 y + ^2 y) + 2( x y + x y) = 1 + 3 1 + 1 + 2 (x+y) = 4 2 (x+y) = 2 (x+y) = 1 This implies that x+y = 2 + 2k , which means y = 2 - x + 2k . Using this relation, we can write: y = ( 2 - x + 2k ) = x y = ( 2 - x + 2k ) = x Substitute these back into the original equations: From (i): x + x = 1 2 x = 1 x = 1 2 From (ii): x + x = 3 2 x = 3 x = 3 2 The un