# The equation of the line passing through the intersection of the lines 2x - 5y + 1 = 0 and 3x + 2y - 8 = 0, and having equal non-zero intercepts

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The equation of the line passing through the intersection of the lines 2x - 5y + 1 = 0 and 3x + 2y - 8 = 0, and having equal non-zero intercepts on the axes, is

(A)  x + y = 3

(B)  x + y = 2

(C)  x + y = 1

(D)  x + y = -3

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Correct option  (A)  x + y = 3

Explanation :

the intersection of the given lines is of the form

(2x - 5y + 1) λ(3x + 2y - 8) = 0

On simplification we get (2 + 3λ)x + (2K - 5)y + 1 8λ = 0

whose intercepts on the axes are

If λ = 1/8 then the line is x - 2y = 0 which is not the case. Hence x =  -7 and the required line is -19x - 19y + 57 = 0 or x + y - 3 = 0

Direct Method: The point of intersection of the given lines is (2, 1). Any line having equal intercepts on the coordinates axes is of the form x + y = a. This line passes through the point (2, 1) which implies that a = 3. Hence the equation of the required line is x + y = 3.