The path of the two rail tracks are represented by the equationsx+ky-4=0,2x+4y-12=0 as shown in the graph are parallel:
 Answer the following:
The value of k for which equations above are parallel
3
4
2
1
The coordinate whose the line 2x+4y-12=0 cuts x-axis&y-axis respectively
(6,0)&(0,3)
(0,6)&(3,0)
(8,0)&(0,4)
(0,8) & (0,4)
The area of the shaded region in sq.units:
3
5
2
1
The pair of equations in graph are:
consistent
inconsistent
consistent&dependent
none of these
Which of the following is not a solution of the equation
2x + 4y – 12 = 0
(0, 3)
(6, 0)
(2, 2)
(4, -1)
Answers
Given : The path of the two rail tracks are represented by the equationsx+ky-4=0,2x+4y-12=0 are parallel:
To Find : Value of k
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)
x+ky-4=0,
2x+4y-12=0
1/2 = k/4 ≠ -4/-12
=> k = 2
1/2 = 1/2 ≠ 1/3
Hence value of k = 2
2x+4y-12=0
x = 0 => y = 3
y = 0 => x = 6
( 6 , 0) and ( 0 , 3)
4, -1 is not a solution of 2x + 4y – 12 = 0
as 8 - 4 - 12 = - 8 ≠ 0
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