Question

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)3/2x+5/3y=7
9x-10y=12

d)5x-3y=11
-10x+6y=-22

e)4/3x+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
​

Answer 1

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

Solve other similarly:

Post question one by one

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