The expression ax + by has value 7 when x = 2 and y = 1. When x = -1, y = 1, it has value 1, find a and b.

Given,

ax + by = 7, when x = 2, y = 1.

⇒ 2a + b = 7 ……(i)

ax + by = 1 when x = -1, y = 1.

⇒ -a + b = 1 …….(ii)

Multiplying eq. (ii) by 2 we get,

⇒ -2a + 2b = 2 …….(iii)

Adding eq. (i) and (iii) we get,

⇒ 2a + b + (-2a + 2b) = 7 + 2

⇒ 2a - 2a + b + 2b = 9

⇒ 3b = 9

⇒ b = 3.

Substituting value of b in eq. (ii) we get,

⇒ -a + 3 = 1

⇒ -a = -2

⇒ a = 2.

Hence, a = 2 and b = 3.