Q5 of 186 Page 3

The path of highway number 1 and 2 are given by the equations x — y = 1 and 2x + 3y = 12 respectively. Represent these equations geometrically.

The given equation is

x – y = 1


and


2x + 3y = 12


Now, let us find atleast two solutions of each of the above equations, as shown in the following tables.


Table for x – y = 1 or y = x – 1



Now, table for 2x + 3y = 12




From the graph, it is clear that lines represented by the equations x – y = 1 and 2x + 3y – 12 = 0 are intersecting at a point A i.e. (3,2)


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3

Present age of father is 30 years more than twice that of his son. After 10 years, the age of father will be thrice the age of his son. Represent this situation algebraically and geometrically.

 4

The path of a wheel of train A is given by the equation x + 2y — 4 = 0 and the path of a wheel of another train B is given by the equation 2x + 4y — 12 = O. Represent this situation geometrically.

 6

Person A walks along the path joining points (0, 3) and (1, 3) and person B walks along the path joining points (0, 4) and (1, 5). Represent this situation geometrically.

 7

Examine which of the following pair of values of x and y is a solution of equation 4x — 3y + 24 = 0.

(i) x = 0, y = 8 (ii) x = — 6, y = 0


(iii) x = 1, y = — 2 (iv) x = – 3,y = 4


(v) x = 1, y = — 2 (vi) x = — 4, y = 2