# 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

(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.

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