Question

What is the equation of the line joining the origin with the point of intersection of the lines 4x + 3y = 12 and 3x + 4y = 12 ?

(a) x + y = 1 

(b) x – y = 1 

(c) 3y = 4x 

(d) x = y

Answer 1

(d) x = y

The equations of the given lines are: 

4x + 3y = 12    ...(i) 

3x + 4y = 12   ...(ii) 

Solving the simultaneous equations (i) and (ii), we get

\(x\) = \(\frac{12}{7}\), y = \(\frac{12}{7}\)

∴ Point of the intersection of the given lines is \(\bigg(\)\(\frac{12}{7}\), \(\frac{12}{7}\)\(\bigg)\)

Now equation of the line passing through (0, 0) and\(\bigg(\)\(\frac{12}{7}\), \(\frac{12}{7}\)\(\bigg)\)is

y - 0 = \(\bigg(\frac{\frac{12}{7}-0}{\frac{12}{7}-0}\bigg)\) (x – 0), i.e., y = x.