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



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