Check whether the following equations are consistent or inconsistent solve them graphically 4/3x+2y=8,2x+3y=12
Answers
Answer:
4/3x+2y-8=0 ____(1)
2x+3y-12=0____(2)
a1/a2=4/3*2=4/6=2/3
b1/b2=2/3
c1/c2=-8/-12=2/3
Therefore, a1/a2=b1/b2=c1/c2
It shows consistent.
Given : (4/3)x + 2y = 8 2x + 3y = 12
To Find : following equations are consistent or inconsistent
Solution:
a₁x + b₁y = c₁
a₂x + b₂y = c₂
Consistent if
a₁/a₂ = b₁/b₂ = c₁/c₂ ( Infinite solution , same line )
or a₁/a₂ ≠ b₁/b₂ ( unique solution , intersecting lines )
Inconsistent if
a₁/a₂ = b₁/b₂≠ c₁/c₂ ( no solution , Parallel lines)
(4/3)x + 2y = 8
2x + 3y = 12
(4/3)/2 = 2/3
2/3
8/12 = 2/3
2/3 = 2/3 = 2/3
( Infinite solution , same line )
Consistent
Draw graph for both equation
Both are same line.
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