Question

Write four solutions for each of the following equations. (1) 2x+y=7 (2) πx+y=9(3) x=4y . This question is how to make in graph.

Answer 1

$\sf \underline{ \large{Solution-} }$

[1] 2 x + y = 7

⟶ By putting x = 0

⟹ 2 (0) + y = 7

⟹ 0 + y = 7

⟹ y = 7

• A(0,7)

⟶ By putting x = 1

⟹ 2 (1) + y = 7

⟹ 2 + y = 7

⟹ y = 7 - 2

⟹ y = 5

• B(1,5)

⟶ By putting y = 0

⟹ 2 x + y = 7

⟹ 2 x + (0) = 7

⟹ 2 x = 7

⟹ x = 7/2

• C(7/2,0)

⟶ By putting y = 1

⟹ 2 x + (1) = 7

⟹ 2 x = 7 - 1

⟹ 2 x = 6

⟹ x = 6/2

• D(3,1)

➢ Hence A(0,7) , B(1,5) , C(7/2,0) and D(3,1) are the four solutions of the equation 2 x + y = 7.

Now,

[2] π x + y = 9

⟶ By putting x = 0  

⟹ π (0) + y = 9

⟹ 0 + y = 9

⟹ y = 9

• A(0,9)

⟶ By putting x = 1

⟹ π (1) + y = 9

⟹ y = 9 - π

• B(1,9 - π)

⟶ By putting x = 3

⟹ π (3) + y = 9

⟹ 3π + y = 9

⟹ y = 9 -  3π

• C(3,9 - 3π)

⟶ By putting x = 4

⟹ π (4) + y = 9

⟹ 4π + y = 9

⟹ y = 9 -  4π

• D(4,9 -  4π)

➢ Hence A(0,9) , B(1,9 - π) , C(3,9 - 3π) and D(4,9 -  4π) are the four solutions of the equation π x + y = 9.

Now,  

[3] x = 4 y

⟶ By putting y = 0

⟹ x = 4 (0)

⟹ x = 0

• A(0,0)

⟶ By putting y = 1

⟹ x = 4 (1)

⟹ x = 4

• B(4,1)

⟶ By putting y = 2

⟹ x = 4 (2)

⟹ x = 8

• C(8,2)

⟶ By putting y = 3

⟹ x = 4 (3)

⟹ x = 12

• D(12,3)

➢ Hence A(0,0) , B(4,1) , C(8,2) and D(12,3) are the four solutions of the equation x = 4 y