Question

Find the equation of a line passing through the point (−3, 2) and the point of intersection of the lines x + y = 3 and x − 2y = 0.

Answer 1

Here, solving the linear equations:

(1) x + y = 3

(2) x − 2y = 0 ⇒ x = 2y

Substitute x = 2y into the first equation:

2y + y = 3

3y = 3

y = `3/3`

∴ y = 1

Now, let's find x:

x = 2y

x = 2(1)

∴ x = 2

The line passes through (−3, 2) and the intersection point (2, 1),

Using the two-point formula:

`(y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1)`

Substituting the points (−3, 2) and (2, 1),

`(y - 2)/(x - (-3)) = (1 - 2)/(2 - (-3))`

`(y - 2)/(x + 3) = (-1)/5`

5(y − 2) = −1(x + 3)    ...[Cross-multiply]

5y − 10 = −x − 3

x + 5y − 10 + 3 = 0

∴ x + 5y − 7 = 0

Hence, the equation of the line is x + 5y − 7 = 0 or x + 5y = 7.