Question

Find the equation of a line passing through the origin and the point of intersection of the lines 3x + y = 7 and x − 2y = −7.

Answer 1

Here, solving the linear equations:

(1) 3x + y = 7 ⇒ y = 7 − 3x

(2) x − 2y = −7

Substitute y from Equation (1) into Equation (2):

x − 2(7 − 3x) = −7

x − 14 + 6x = −7

x + 6x = −7 + 14

7x = 7

x = `7/7`

∴ x = 1

Substitute x = 1 back into Equation (1):

y = 7 − 3(1)

= 7 − 3

∴ y = 4

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

`m = (y_2 - y_1)/(x_2 - x_1)`

= `(4 - 0)/(1 - 0)`

∴ m = 4

Using the point-slope formula:

y = mx

y = 4x

Let’s rearrange the above equation in standard form (Ax + By + C = 0):

4x − y = 0

Hence, the equation of a line is 4x − y = 0.