Check whether the following equations are consistent or inconsistent

Asked by admin @ 16/08/2021 in Math viewed by 320 People

Check whether the following equations are consistent or inconsistent. Solve them graphically.

a) 3x+2y=5 2x - 3y = 7
b) 2x - 3y = 8 4x -6y = 9
c) 3/2 x + 5/3 y = 7 9x - 10y=14
d) 5x-3y = 11 -10x+6y = -22
e) x +2y = 8 2x+3y = 12
f) x + y = 5 2x+2y = 10
g) x - y = 8 3x-3y = 16
h) 2x + y-6 = 0 4x-2y- 4 = 0
i) 2x-2y - 2 = 0 4x-4y- 5 = 0

Answered by admin @ 16/08/2021

Given : 3x+2y=5 , 2x-3y=7

To find : equations are consistent or inconsistent.

Solution:

a₁x+ b₁y=c₁

a₂x+b₂y=c₂

Consistent

if a₁/a₂ ≠ b₁/b₂ ( unique solution)

a₁/a₂ = b₁/b₂ = c₁/c₂ ( infinite solution )

Inconsistent

if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution)

3x+2y=5

2x-3y=7

3/2 ≠ 2/3

Hence consistent

unique solution

y = -11/13

x = 29/13

Graph attached

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