Question

1. Solve graphically the following pairs of linear equations :
(i) 2x - y = 4 , 3y - x = 3 . Also find the coordinates of the points where these lines intersect te 2 axes .
(ii) 2x + 3y = 12 , x - y = 1. Shade the region (area) between the 2 lines and x axis.​

Answer 1

EXPLANATION.

Graphically the pair of linear equation.

Question = 1.

⇒ 2x - y = 4. - - - - - (1).

⇒ 3y - x = 3. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ 2x - y = 4. - - - - - (1).

Put the value of x = 0 in the equation, we get.

⇒ 2(0) - y = 4.

⇒ - y = 4.

⇒ y = - 4.

Their Co-ordinates = (0,-4).

Put the value of y = 0 in the equation, we get.

⇒ 2x - (0) = 4.

⇒ 2x = 4.

⇒ x = 2.

Their Co-ordinates = (2,0).

From equation (2), we get.

⇒ 3y - x = 3. - - - - - (2).

Put the value of x = 0 in the equation, we get.

⇒ 3y - (0) = 3.

⇒ 3y = 3.

⇒ y = 1.

Their Co-ordinates = (0,1).

Put the value of y = 0 in the equation, we get.

⇒ 3(0) - x = 3.

⇒ - x = 3.

⇒ x = - 3.

Their Co-ordinates = (-3,0).

Both curves intersects at a point = (3,2).

Question = 2.

⇒ 2x + 3y = 12. - - - - - (1).

⇒ x - y = 1. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ 2x + 3y = 12. - - - - - (1).

Put the value of x = 0 in the equation, we get.

⇒ 2(0) + 3y = 12.

⇒ 3y = 12.

⇒ y = 4.

Their Co-ordinates = (0,4).

Put the value of y = 0 in the equation, we get.

⇒ 2x + 3(0) = 12.

⇒ 2x = 12.

⇒ x = 6.

Their Co-ordinates = (6,0).

From equation (2), we get.

⇒ x - y = 1. - - - - - (2).

Put the value of x = 0 in the equation, we get.

⇒ (0) - y = 1.

⇒ - y = 1.

⇒ y = - 1.

Their Co-ordinates = (0,-1).

Put the value of y = 0 in the equation, we get.

⇒ x - (0) = 1.

⇒ x = 1.

Their Co-ordinates = (1,0).

Both curves intersects at a point = (3,2).

Answer 2

Step-by-step explanation:

1.(a) 2x-y=4

(i)Putting x=0

0-y=4

-y=4

y=-4

Their co-ordinate=(0,-4)

(ii)Putting y=0

2x-0=4

2x=4

x=2

Their co-ordinate=(2,0)

(b) 3y-x=3

(i)Putting y=0

0-x=3

-x=3

x=-3

Their co ordinate=(-3,0)

(ii) Putting x=0

3y-0=3

3y=3

y=1

Their co-ordinate=(0,1)

2.(a) 2x+3y=12

(i)Putting x=0

0+3y=12

3y=12

y=4

Their co-ordinate=(0,4)

(ii) Putting y=0

2x+0=12

2x=12

x=6

Their co-ordinate=(6,0)

(b) x-y=1

(i)Putting x=0

0-y=1

-y=1

y=-1

Their co-ordinate=(0,-1)

(ii) putting y=0

x-0=1

x=1

Their co-ordinate=(1,0)