check graphically whether the pair of equations 3x-2y+2=0 and 3/2x-y+3=0 is consistent .also find the coordinate of the points where the graphs of the equation meet the y axis
Answers
Given : the pair of equations 3x-2y+2=0 and 3/2x-y+3=0
To find : check graphically whether it is consistent .
The coordinate of the points where the graphs of the equation meet the y axis
Solution:
pair of linear equation
Consistent if unique solution or infinite solution
pair of linear equation
Inconsistent if no solution
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
if a₁ /a₂ ≠ b₁/b₂ Consistent & unique solution (Intersecting lines)
a₁ /a₂ = b₁/b₂ ≠ c₁/c₂ Inconsistent having no solution ( Parallel lines )
a₁ /a₂ = b₁/b₂ = c₁/c₂ Consistent having infinite solution ( coinciding lines )
3x - 2y + 2 = 0
(3/2)x - y + 3 = 0
=> 3/(3/2) = 2
- 2/-1 = 2
2/3
2 = 2 ≠ 2/3
Hence inconsistent
not consistent
Parallel lines
From Graph also line s are parallel
3x - 2y + 2 = 0 meets y axis at (0,1)
(3/2)x - y + 3 = 0 meets y axis at (0,3)
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