Find the equation of the line drawn through the point of intersection of the lines x – y = 7 and 2x + y = 2 and passing through the origin.
Suppose the given two lines intersect at a point P(x1, y1). Then, (x1, y1) satisfies each of the given equations.
x – y = 7 …(i)
2x + y = 2 …(ii)
Now, we find the point of intersection of eq. (i) and (ii)
Multiply the eq. (i) by 2, we get
2x – 2y = 14 …(iii)
On subtracting eq. (iii) from (ii), we get
2x – 2y – 2x – y = 14 – 2
⇒ – 3y = 12
⇒ y = -4
Putting the value of y in eq. (i), we get
x – (-4) = 7
⇒ x + 4 = 7
⇒ x = 7 – 4
⇒ x = 3
Hence, the point of intersection P(x1, y1) is (3, -4)
Let AB is the line drawn from the point of intersection (3, -4) and passing through the origin.
Firstly, we find the slope of the line joining the points (3, -4) and (0, 0)
Now, we have to find the equation of the line passing through the origin
Equation of line: y – y1 = m(x – x1)
⇒ 4x + 3y = 0
Hence, the equation of the line passing through the origin is 4x + 3y = 0