Question

2
Draw
the
graphs of
of the equations
x+y=2 & 2x+y=1
.​

Answer 1

EXPLANATION.

Graph of the equation.

⇒ x + y = 2. - - - - - (1).

⇒ 2x + y = 1. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ x + y = 2. - - - - - (1).

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

⇒ (0) + y = 2.

⇒ y = 2.

Their Co-ordinates = (0,2).

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

⇒ x + (0) = 2.

⇒ x = 2.

Their Co-ordinates = (2,0).

From equation (2), we get.

⇒ 2x + y = 1. - - - - - (2).

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

⇒ 2(0) + y = 1.

⇒ y = 1.

Their Co-ordinates = (0,1).

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

⇒ 2x + (0) = 1.

⇒ 2x = 1.

⇒ x = 1/2.

⇒ x = 0.5

Their Co-ordinates = (0.5,0).

Both curves intersects at a point = (-1,3).

Answer 2

Answer: Please check attached image.

Step-by-step explanation:

x + y = 2... (i)

x = 0, y = 2

x = 2, y = 0

2x + y = 1... (ii)

x = 0, y = 1

x = 1/2, y = 0

Now, to find intersection...

Subtract equation (i) from (ii)

2x + y - (x + y) = 1 - 2

2x + y - x - y = -1

x = -1

Put x = -1 in equation (i)

x + y = 2

-1 + y = 2

y = 2 + 1

y = 3

Now, drawing graph:

(Please check attached image)

Thanks.