Q5 of 62 Page 25

Two straight paths are represented by the equations and Check whether the paths cross each other or not.

Given linear equations are

x - 3y - 2 = 0 …(i)


and -2x + 6y - 5 = 0 …(ii)


On comparing with ax + by c=0, we get


Here, a1 =1, b1 =-3, c1 =- 2;


And a2 = -2, b2 =6, c2 =- 5;





i.e., a1/a2 = b1/b2 c1/c2 [parallel lines]


Hence, two straight paths represented by the given equations never cross each other, because they are parallel to each other.


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For which values of a and b will the following pair of linear equations has infinitely many solutions?

x + 2y = 1 and (a - b)x + (a + b)y = a + b – 2

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Find the values of p in (i) to (iv) and p and q in (v) for the following pair of equations

(i) 3x - y - 5 = 0 and 6x - 2y - p = 0, if the lines represented by these equations are parallel.


(ii) -x + py = 1 and px - y - 1 = 0, if the pair of equations has no solution.


(ii) -3x + 5y = 7 and 2px - 3y = 1, if the lines represented by these equations are intersecting at a unique point.


(iv) 2x +3y - 5 = 0 and px - 6y - 8 = 0, if the pair of equations has a unique solution.


(v) 2+3y =7 and 2px + py = 28 - qy, if the pair of equations has infinitely many solutions.

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Write a pair of linear equations which has the unique solution x = - 1 and y = 3. How many such pairs can you write?

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If 2x + y = 23 and 4x - y = 19 then find the values of 5y - 2x and