Question

The equation of the straight line passing through the point (2, –2) and the point of intersection of the lines 5x – y = 9 and x + 6y = 8 is

• A. y – 2 = 0
• B. y + 2 = 0
• C. x – 2 = 0
• D. x + 2 = 0

Answer 1

The correct option is C

x – 2 = 0

Equation of any line passing through the point of intersection of given lines is

(5x – y – 9) + k(x + 6y – 8) = 0 …… (1)

Since it passes through the point (2, –2),

$\therefore$ (5 $\times$ 2 + 2 – 9) + k(2 – 12 – 8) = 0 or k = $\frac{1}{6}$

Putting the value of k in equation (1), the equation of the required line is

(5x – y – 9) + $\frac{1}{6}$ (x + 6y – 8) = 0 or 31x – 62 = 0

or x – 2 = 0