Question

The value of k for which the lines 5x+7y=3 and 15x + 21y = k coincide is (a) 9 (b) 5 (c) 7 (d) 18
Grade 10

Answer 1

Given: Lines 5x+7y=3 and 15x + 21y = k coincide  

To Find : value of k

(a) 9 (b) 5 (c) 7 (d) 18

Solution:

Pair of linear equations

a₁x  +  b₁y + c₁  =  0

a₂x  +  b₂y + c₂  =  0

Consistent

if a₁/a₂ ≠ b₁/b₂   (unique solution  and lines intersects each others)

  a₁/a₂ = b₁/b₂ = c₁/c₂   (infinite solutions and line coincide each other )

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution , lines are parallel to each other)

5x+7y=3 and 15x + 21y = k coincide

=> 5/15 = 7/21 = 3/k

=> 1/3 = 1/3  = 3/k

=> k = 9

Hence the value of k is 9

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