Question

"Question 2 Write four solutions for each of the following equations: (i) 2x + y = 7 (ii) πx + y = 9 (iii) x = 4y

Class 9 - Math - Linear Equations in Two Variables Page 70"

Answer 1

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....

Answer 2

Hey I'm MrMysterious

The answer of your Question is ->

≥
(i) 2x + y = 7
⇒ y = 7 - 2x
→ Put x = 0,
y = 7 - 2 × 0 ⇒ y = 7
(0, 7) is the solution.
→ Now, put x = 1
y = 7 - 2 × 1 ⇒ y = 5
(1, 5) is the solution. 
→ Now, put x = 2
y = 7 - 2 × 2 ⇒ y = 3
(2, 3) is the solution. 
→ Now, put x = -1
y = 7 - 2 × -1 ⇒ y = 9
(-1, 9) is the solution.
The four solutions of the equation 2x + y = 7 are (0, 7), (1, 5), (2, 3) and (-1, 9).

(ii) πx + y = 9
⇒ y = 9 - πx 
→ Put x = 0,
y = 9 - π×0 ⇒ y = 9
(0, 9) is the solution.
→ Now, put x = 1
y = 9 - π×1 ⇒ y = 9-π
(1, 9-π) is the solution. 
→ Now, put x = 2
y = 9 - π×2 ⇒ y = 9-2π
(2, 9-2π) is the solution. 
→ Now, put x = -1
y = 9 - π× -1 ⇒ y = 9+π
(-1, 9+π) is the solution.
The four solutions of the equation πx + y = 9 are (0, 9), (1, 9-π), (2, 9-2π) and (-1, 9+π).

(iii) x = 4y
→ Put x = 0,
0 = 4y ⇒ y = 0
(0, 0) is the solution.
→ Now, put x = 1
1 = 4y ⇒ y = 1/4
(1, 1/4) is the solution. 
→ Now, put x = 4
4 = 4y ⇒ y = 1
(4, 1) is the solution. 
→ Now, put x = 8
8 = 4y ⇒ y = 2
(8, 2) is the solution.
The four solutions of the equation πx + y = 9 are (0, 0), (1, 1/4), (4, 1) and (8, 2)


✴Brainly Benefactor✴
From MrMysterious