Q. 34.0( 2 Votes )

Find the equation

Answer :

Suppose the given two lines intersect at a point P(x1, y1). Then, (x1, y1) satisfies each of the given equations.

x + y = 9 …(i)


2x – 3y + 7 = 0 …(ii)


Now, we find the point of intersection of eq. (i) and (ii)


Multiply the eq. (i) by 2, we get


2x + 2y = 18


or 2x + 2y – 18 = 0 …(iii)


On subtracting eq. (iii) from (ii), we get


2x – 3y + 7 – 2x – 2y + 18 = 0


-5y + 25 = 0


-5y = -25


y = 5


Putting the value of y in eq. (i), we get


x + 5 = 9


x = 9 – 5


x = 4


Hence, the point of intersection P(x1, y1) is (4, 5)



Now, we have to find the equation of the line passing through the point (4, 5) and having slope


Equation of line: y – y1 = m(x – x1)




2x + 3y – 15 – 8 = 0


2x + 3y – 23 = 0


Hence, the equation of line having slope -2/3 is 2x + 3y – 23 = 0



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