Question

How many solutions can find for :-
2x + 2y = 12

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Answer 1

Question :-

How many solutions can you find for :-

2x + 2y = 12

Solution :-

You may find 3 solutions for the given Equation;

1st Solution :-

x = 3

y = 3

As,

2*3 + 2*3 = 12

6 + 6 = 12

12 = 12

LHS = RHS

2nd Solution :-

x = 2

y = 4

As,

2*2 + 2*4 = 12

4 + 8 = 12

12 = 12

LHS = RHS

3rd Solution :-

x = 1

y = 5

As,

2*1 + 2*5 = 12

2 + 10 = 12

12 = 12

LHS = RHS

Thank You*

Answer 2

Answer:

Let us consider the value of x as 1 :

2(1) + 2y = 12

2 + 2y    = 12

2y =  12 - 2

2y = 10

y = 10/2

y = 5

Thus (x,y) = (1,5) where x=1 and y=5

Let us consider the value of x as 2

2(2) + 2y = 12

4 + 2y = 12

2y = 12 -4

2y = 8

y = 8/2

y = 4

Thus (x,y) = (2,4) where x=2 and y=4

Let the value of x be 0

2(0) +2y= 12

0 + 2y = 12

2y = 12

y = 12/2

y = 6

Thus (x,y) = (0,6) where x=0 and y=6

Let the value of x be anything , we will surely find some or the other solution . The value of x keeps on changing , changing the value of y and vice versa.

Thus we can conclude that any linear equation in 2 variables can have infinite solutions .

Hence , the given equation 2x+2y = 12 can have infinite solutions.