Question

Solve the following pair of equation graphically: 2x-y=10 and x-3y=15.

Also shade the triangular region formed by the above lines and x- axi​

Answer 1

EXPLANATION.

Pair of linear equation Graphically.

⇒ 2x - y = 10. - - - - - (1).

⇒ x - 3y = 15. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ 2x - y = 10. - - - - - (1).

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

⇒ 2(0) - y = 10.

⇒ - y = 10.

⇒ y = - 10.

Their Co-ordinates = (0,-10).

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

⇒ 2x - (0) = 10.

⇒ 2x = 10.

⇒ x = 5.

Their Co-ordinates = (5,0).

From equation (2), we get.

⇒ x - 3y = 15. - - - - - (2).

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

⇒ (0) - 3y = 15.

⇒ - 3y = 15.

⇒ 3y = - 15.

⇒ y = - 5.

Their Co-ordinates = (0,-5).

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

⇒ x - 3(0) = 15.

⇒ x = 15.

Their Co-ordinates = (15,0).

Both curves intersects at a point = (3,-4).

Answer 2

Given :-

2x - y = 10

x - 3y = 15

To Find :-

x and y

Solution :-

In 1

Putting the value of x as 0

$\sf 2(0) - y = 10$

$\sf 0-y=10$

$\sf -y=10$

$\sf y=-10$

Then

Co-ordinates = (0,-10)

Putting the value of y as 0

$\sf 2x-0=10$

$\sf 2x=10$

$\sf x=\dfrac{10}{2}$

$\sf x=5$

Then

Co-ordinate = (5,0)

In equation 2

Putting the value of x as 0

$\sf 0-3y=15$

$\sf -3y=15$

$\sf -y=\dfrac{15}{3}$

$\sf -y=5$

$\sf y =-5$

Then

Co-ordinate = (0,-5)

Putting the value of y as 0

$\sf x-3(0)=15$

$\sf x=15$

Then

Co-ordinate = (15,0)