Question

the co-ordinate of point intercept of line ax+ b y = 7 and b x + a y= 5 is (3,1) find the value of a and b​

Answer 1

$(x \: y) = (3 \: \: 1) \\ x = 3 \\ y = 1 \\ ax + by = 7 \\ a \times 3 + b \times 1 = 7 \\ 3a + b = 7 - - - (1) \\ bx + ay = 5 \\ b \times 3 + a \times 1 = 5 \\ 3b + a = 5 \\ a + 3b = 5 - - - (2) \\ mutiple \: eqn \: (1) \: by \: 3 \\ 9a + 3b = 21 - - - (3) \\ subtract \: eqn \: (2) \: \: from \: (3) \\ hence \: 8a = 16 \\ a = 2 \\ b = 1$