Question

Find the equation of the straight line passing through the point (2, 1) and through the point of Intersection of the lines x + 2y = 3 and 2x – 3y= 4.

• A. 5x + 3y – 13 = 0
• B. 4x – 7y – 1= 0
• C. 2x – 7y – 20=0
• D. x – 7y + 13 =0

Answer 1

The correct option is A 5x + 3y – 13 = 0

1^st method: - equation of any straight line passing through the intersection of the lines x + 2y = 3 and 2x – 3y= 4 is

(x + 2y – 3) + (2x – 3y – 4) = 0

Since it passes through the point (2, 1)

(2 + 2 – 3) + (4 – 3 – 4) = 0

- 3 = 0

= 3

Now substituting this value of in (i), we get

3(x + 2y – 3) + (2x – 3y – 4) = 0

5x + 3y – 13 = 0

2^nd method: - The straight line passing through the point (2, 1), put x = 2 and y = 1only option (a) and (b) will satisfy. Now, intersection point of the lines x + 2y = 3 and 2x – 3y= 4 is (), Put x = and y = only option(a) will satisfy. Option(a).