Find, which of the following points lie on the line x - 2y + 5 = 0 :

(i) (1, 3) (ii) (0, 5)

(iii) (-5, 0) (iv) (5, 5)

(v) (2, -1.5) (vi) (-2, -1.5)

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Solve graphically each of the following systems of linear equations. Also find the coordinates of the points where the lines meet axis of y.

(i) 2x - 5y + 4 = 0,

2x - y - 8 = 0

(ii) 3x + 2y = 12

5x - 2y = 4

(iii) 2x + y - 11 = 0,

x - y - 1 = 0

(iv) x + 2y - 7 = 0

2x - y - 4 = 0

(v) 3x + y - 5 = 0

2x - y - 5 = 0

(vi) 2x - y - 5 = 0

x - y - 3 = 0

2 x^{2} - 8 x + 5 = 0

3 x^{2} - 2 \sqrt{6} x + 2 = 0

5 x^{2} - 4 x + 1 = 0

5 x (x - 2) + 6 = 0

12 x^{2} - 4 \sqrt{15} x + 5 = 0

x^{2} - x + 2 = 0

Find the nature of the roots of the following quadratic equations:
(i) $2 x^{2} - 8 x + 5 = 0$

(ii) $3 x^{2} - 2 \sqrt{6} x + 2 = 0$
(iii) $5 x^{2} - 4 x + 1 = 0$

(iv) $5 x (x - 2) + 6 = 0$
(v) $12 x^{2} - 4 \sqrt{15} x + 5 = 0$

(vi) $x^{2} - x + 2 = 0$

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