Math, asked by xeneron576, 10 months ago

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

Answered by kotipallirajkumar345
4

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.        

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