Q. 415.0( 2 Votes )

# Find the solutions of the form x = a, y = 0 and x = 0, y = b for each of the following pairs of equations.

Do they have any common such solution?

(i) 3x + 2y = 6 and 5x - 2y =10

(ii) 5x + 3y = 15 and 5x + 2y =10

(iii) 9x + 7y = 63 and x - y =10

Answer :

(i) 3x+2y = 6 and 5x-2y = 10

Put y = 0, 3x+ 2൰ = 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.

Put y = 0, 3x+ 2൰ = 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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