Question

which of the following pair of linear equation are consistent or inconsistnet
x+y =5,2x +2y=10

Answer 1

Answer:

(i) x+y=5 ...(i)

2x+2y=10 ...(ii)

⇒x+y=5

⇒y=5−x

x 0 3

y 5 2

Plot (0,5) and (3,5) on graph and join them to get equation x+y=5.

2x+2y=10

⇒2y=(10−2x)

⇒y=

2

10−2x

=5−x ...(iii)

x 5 2

y 0 3

So, the equation is consistent and has infinitely many solution

(ii) x−y=8 ....(i)

3x−3y=16 ....(ii)

⇒x−y=8

⇒−x+y=−8

⇒y=−8+x

⇒y=x−8

x 8 0

y 0 -8

3x−3y=16 ...(ii)

⇒3x=16+3y

⇒3x−16=3y

⇒y=

3

3x−16

⇒y=x−

3

16

x

3

16

0

y 0

3

−16

Plotting both the equation in graph, we see that the lines are parallel , so inconsistent.

(iii) 2x+y−6=0

4x−2y−4=0

2x+y=6 ....(i)

4x−2y=4 ...(ii)

For equation (i), 2x+y=6⇒y=6−2x

x 0 3

y 6 0

Plot point (0,6) and (3,0) on a graph and join then to get equation 3x+y=6

For equation (ii), 4x−2y=4⇒

2

4x−4

=y

x 1 0

y 0 −2

Plot point (1,0) and (0,−2) on a graph and join them to get equation 4x−2y=0

x=2,y=2 is the solution of the given pairs of equation . So. solution is consistent.

(iv) 2x−2y=2 ...(i)

4x−4y=5 ...(ii)

2x−2y=2⇒2x−2=2y

y=x−1

x 0 1

y −1 0

Plot point (0,1) and (1,0) and join to get the equation 2x−2y=2 on a graph 4x−4y=5⇒4x−5=4y

⇒

4

4x−5

=y

x 0

4

5

y −

4

5

0

Plot point (0,−

4

5

) and (

4

5

,0) and join them to get the equation 4x−4y=5 on a graph.

The two lines never intersect, so, the solution is inconsistent.

Step-by-step explanation:

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