Question

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically.
(i) x + y = 5, 2x + 2y = 10
(ii) x-y – 8, 3x – 3y = 16
(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0
(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
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Answer 1

Answer:

The Second, Fourth one is inconsistent:

Explanation:

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

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

On rearranging the variables in (i)

You get y=5-x

So the(x,y) pair will be

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= (10−2x)/2 =5−x ...(iii)

Next Pair

x 5 2

y 0 3

Plot (5,0) and (5,3) on graph and join them to get equation 2x+2y=10

So, the equation is consistent and has infinitely many solution

(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⇒

2y=4x−4

y=(4x-4)/2

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.

Hope This Helps........