Question

Solve the given pair of linear equations,

2^x + 3^y = 17 

2^x+2 – 3^y+1 = 5

Answer 1

Given: 2^x + 3^y = 17 and 

2^x+2 – 3^y+1 = 5 

Take 2^x = a and 3^y = b then the given equations reduce to 

2^x + 3^y = 17 ⇒ a + b = 17 …… (1) 

2^x . 2² – 3^y . 3 = 5 ⇒ 4a – 3b = 5 …… (2)

Substituting b = 9 in equation (1) we get 

a + 9 = 17 ⇒ a = 17 – 9 = 8 

But a = 2^x – 8 and b = 3^y = 9 

⇒ 2^x = 2³ and 3^y = 3² 

⇒ x = 3 and y = 2 

∴ The solution (x, y) is (3, 2).