Find the equation of the line passing through the point of intersection of `2x-7y+11=0\ a n d\ x+3y-8=0\ ` and is parallel to i. x-axis ii. y-axis.

Explanation

Given: The equations, `2x – 7y + 11 = 0` and` x + 3y – 8 = 0 `

The equation of the straight line passing through the points of intersection of` 2x − 7y + 11 = 0` and `x + 3y − 8 = 0` is given below:

`2x − 7y + 11 + lambda(x + 3y − 8) = 0`

`(2 + lambda)x + (− 7 + 3lambda)y + 11 − 8lambda = 0`

(i) The required line is parallel to the x-axis.

So, the coefficient of x should be zero. `2 + lambda = 0`

`lambda = -2`

Now, substitute the value of lambda back in equation, we get `0 + (− 7 − 6)y + 11 + 16 = 0`

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