Write four solution for each of the following equation

For finding the solutions of linear equation in
two variables we use the following steps:

1.Put an  put an arbitrary
value of x or y in given equation and find the corresponding value of other
variable.

 Thus, we
get one pair of  solution of given
equation.

2.Repeat  repeat step 1 for
another arbitrary value of x or y and get other pair of solution of given
equation.

For convenience , we put x= 0 & get
corresponding value of y to find one pair of solution.

Also we put y = 0 and get corresponding value of
x to find 2nd pair solution.

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Solution:

(a)2x + y = 7......(1)

On putting x=0 in equation 1

2x+y=7

2×0+y=7

0+y=7

Y=7

So( 0, 7) is a solution of given equation.

let y=0

2x+y=7

2x+0=7

2x=7

X= 7/2

So(7/2,0) is a solution of given equation.

let x = 1

2x+y=7

2×1+y=7

2+y=7

Y= 7-2

Y=5

(1,5) is the solution.

let x = 2

2x+y=7

2×2+y=7

4+y=7

Y= 7-4

Y= 3

The solution is (2,3)

Hence, 4 out of the infinitely many solutions of
the given equation are(0,7), (7/2,0),(1,5),(2,3)

(b) πx + y = 9

let x = 0

πx + y = 9

π×0+y =9

0+y= 9

Y=9

 (0,9) is
the solution.

Let y = 0

πx + y = 9

πx+0=9

πx=9

x= 9/π

 (9/π,0) is
the solution.

Let x = 1

πx + y = 9

π×1+y=9

π+y=9

Y= 9-π

(1,9-π) is the solution.

Let x = -1

πx + y = 9

π×-1+y=9

-π+y=9

Y= 9+π

 (-1,9+π)
is the solution.

Hence, 4 out of the infinitely many solutions of
the given equation are(0,9), (9/π,0),(1,9-π),(-1,9+π)

(c) x= 4y

Let x = 0

X=4y

0=4y

Y=0/4=0

Y=0

(0,0) is the solution.

Let x= 1

X=4y

1=4y

Y= 1/4

(1,1/4) is the solution.

Let y = 1

X=4y

X=4×1

X=4

(4,1) is the solution.

Let x = 2

X=4y

2=4y

Y=2/4

Y=1/2

(2,1/2) is the solution.

Hence, 4 out of the infinitely many solutions of
the given equation are(0,0), (1,1/4),(4,1),(2,1/2)

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Hope this will help you....