Matrices and Determinants 4 Question 5

5. If the system of linear equations x2y+kz=1,2x+y+z=2,3xykz=3 has a solution (x,y,z),z0, then (x,y) lies on the straight line whose equation is

(2019 Main, 8 April II)

(a) 3x4y4=0

(b) 3x4y1=0

(c) 4x3y4=0

(d) 4x3y1=0

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Answer:

Correct Answer: 5. (c)

Solution:

  1. Given system of linear equations

x2y+kz=12x+y+z=2 and 3xykz=3

has a solution (x,y,z),z0.

On adding Eqs. (i) and (iii), we get

x2y+kz+3xykz=1+34x3y=44x3y4=0

This is the required equation of the straight line in which point (x,y) lies.



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