Find the solutions of the form x=a,y=0 and x=0,y=b for the following pairs of equations .Do they have any common such solutions?
Answers
Answer:
Step-by-step explanation:
(i) 3x+2y = 6 and 5x-2y = 10
Put y = 0, 3x+ 2y = 6 or 3x = 6 ∴ x = 2 Put x = 0 in 3x+2y = 6 3 × 0+2 × y = 6 2y = 6 y = 3∴ The solutions of the equation 3x+2y = 6 is x = 2, y = 0 and x = 0, y = 3. 5x-2y = 10 Take y = 0, 5x-2 × 0 = 10 or 5x = 10 ∴ x = 2. Put x = 0 in 5x-2y = 10 5 × 0-2y = 10, ⇒ -2y = 10 ∴ y = -5, The solutions of the equation 5x-2y = 10 are x = 2, y = 0; x = 0, y = -5. ∴ The solution x = 2, y = 0 is common to both the equations.(ii) 5x+3y = 15 and 5x+2y = 10 5x+3y = 15 Put y = 0 in 5x+3 × 0 = 15 or 5x = 15 ∴ x = 3 Put x = 0 in 5x+3y = 15 5 × 0+3y = 15 ⇒ 3y = 15 ∴ y = 5 The solutions of the equation 5x+3y = 15 are x = 3, y = 0 and x = 0, y = 5.∴The solution x = 0, y = 5 is common to both the equations. Put y = 0 in 5x+2y = 10 5x+2 × 0 = 10 ⇒ 5x = 10 ∴ x = 2 Put x = 0 in 5x+2y = 10 5 × 0+2y = 10 2y = 10 y = 5∴ The solutions of the equation 5x+2y = 10 are x = 2, y = 0 and x = 0, y = 5.(iii) 9x+7y = 63 and x - y = 10 Put y = 0 in 9x+7y = 63 9x+7 × 0 = 63 ⇒ 9x = 63 ∴ x = 7 Put x = 0 in 9x+7y = 63 9 × 0+7y = 63 ⇒ 7y = 63 ∴ y = 9 The solutions of the equation 9x+7y = 63 are x = 7, y = 0 and x = 0, y = 9. Put y = 0 in x - y = 10 x - 0 = 10 ∴ x = 10 Put x = 0 in x- y = 10 0 - y = 10 ∴ y = -10 The solutions of the equation x - y = 10 are x = 10, y = 0 and x = 0, y = -10. ∴ There is no solution common to both the equations.