Question

The point of intersection of lines representing the equation 3x = 2y + 1 and 2x = 3y - 1 is a) (2,3)
b) (3,2)
c) (1,1)
d) (0,0)
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Answer 1

Let the equations be (i) and (ii),

3x = 2y + 1 -------------- (i)

2x = 3y - 1 --------------- (ii)

Subtracting (ii) from (i),

3x - 2x = 2y + 1 - 3y + 1

x = - y + 2 or x = 2 - y -------------- (iii)

Putting (iii) in (i),

3x = 2y + 1

3(2 - y) = 2y + 1

6 - 3y = 2y + 1

5 = 5y

y = 1

From the given options, it can be clearly seen that answer is c) (1,1).