Q. Determine Graphically whether the following system of
linear equations has a Unique solution, No solution or
Infinitely many solutions :
1. 2 x - y = 2, & 4 x - y = 8
2. 2 x - y = 2 & x - y/2 = 6
2. 2x - y = 2 & x/2 - y/4 = 1/2
Answers
Given : system of linear equations
1. 2 x - y = 2, & 4 x - y = 8
2. 2 x - y = 2 & x - y/2 = 6
3. 2x - y = 2 & x/2 - y/4 = 1/2
To find : whether Unique solution, No solution or Infinitely many solutions
Solution:
Graphically
2x - y = 2 4 x - y = 8 x - y/2 = 6 x/2 - y/4 = 1/2
x y y y y
0 -2 -8 -12 -2
1 0 -4 -10 0
2 2 0 -8 2
3 4 4 -6 4
4 6 8 -4 6
2 x - y = 2, & 4 x - y = 8 intersects at x = 3 , y = 4 - Unique solution
2 x - y = 2 & x - y/2 = 6 parallel lines - no solution
2x - y = 2 & x/2 - y/4 = 1/2 Same lines - infinite solution
2x - y = 2
4x - y = 8
=> 2x = 6
=> x = 3
& y = 4
( unique solution )
2 x - y = 2
x - y/2 = 6 => 2x - y = 12
2 ≠ 12
no solution
2x - y = 2
x/2 - y/4 = 1/2 => 2x - y = 2 ( same line)
infinite solution
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