Find the points of intersection of the lines 4x + 3y = 5 and x = 2y – 7.

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

4x + 3y = 5


or 4x + 3y – 5 = 0 …(i)


and x = 2y – 7


or x – 2y + 7 = 0 …(ii)


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


Multiply the eq. (ii) by 4, we get


4x – 8y + 28 = 0 …(iii)


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


4x – 8y + 28 – 4x – 3y + 5 = 0


-11y + 33 = 0


-11y = -33



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


4x + 3(3) – 5 = 0


4x + 9 – 5 = 0


4x + 4 = 0


4x = -4


x = -1


Hence, the point of intersection P(x1, y1) is (-1, 3)


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