Question

If the points A (3,5) and B (1, 4) lie on the graph of the line ax + by = 7, find the values of a and b. SOLUTION It is given that the points A (3. 5) and B (14) lie on the graph of the line. ​

Answer 1

Answer:

Given that A(3, 5) and B(1, 4) lie on the graph of the line ax + by =7 → (1) Hence both the points satisfy the given equation Put x = 3 and y =5 in (1) ⇒ 3a + 5b = 7 → (2) Similarly, B(1, 4) satisfy (1) Put x = 1 and y = 4 in (1), we get a + 4b = 7 Multiply above equation with '3', we get 3a + 12b = 21→ (3) Subtract (2) and (3) 3a + 12b = 21 3a + 5b = 7 --------------- 7b = 14 ∴ b = 2 Put b = 2 in (2), we get 3a + 5(2) = 7 ⇒ 3a = – 3 ∴ a = –1.