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) 3/2 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

Answer 1

For the given system of equations, we have to check if the equations are consistent or inconsistent. To solve that graphincally, we just need to graph both and see if both lines area parallel then system will in inconsistent. if both lines cross each other or overlap then system in consistent.

Ans(a):

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

you can plug any number say x=0 or 1 to find the y-value

plug x=0 into 3x+2y=5

3*0+2y=5

2y=5

y=5/2

so the first point is (0,5/2)

similarly we can find one more point at x=1 as

3x+2y=5

3*1+2y=5

2y=5-3

2y=2

y=1

so the 2nd point is (1,1)

Now join points (0,5/2) and (1,1) by a line

similarly we can graph other equation 2x-3y=7

We are getting intersecting lines so solution is Consistent.

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You can repeat same process for other problems to find the answer:

b) 2x - 3y = 8 4x -6y = 9   [ Inconsistent ]

c) 3/2 x + 5/3 y = 7 9x - 10y=14  [ Consistent ]

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

e) x +2y = 8 2x+3y = 12  [ Consistent ]

f) x + y = 5 2x+2y = 10  [ Consistent ]

g) x - y = 8 3x-3y = 16  [ Inconsistent ]

h) 2x + y-6 = 0 4x-2y- 4 = 0  [ Consistent ]

i) 2x-2y - 2 = 0 4x-4y- 5 = 0 [ Inconsistent ]

Answer 2

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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