Question

18. Solve the following system of equations graphical
3x - y = 3
x - 2y = 4.
Shade the area of the region bounded by the line
and x-axis.
Also, find the area of the shaded region.​

Answer 1

EXPLANATION.

System of equation as graphically.

⇒ 3x - y = 3. - - - - - (1).

⇒ x - 2y = 4. - - - - - (2).

As we know that,

From equation (1), we get.

⇒ 3x - y = 3. - - - - - (1).

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

⇒ 3(0) - y = 3.

⇒ - y = 3.

⇒ y = - 3.

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

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

⇒ 3x - (0) = 3.

⇒ 3x = 3.

⇒ x = 1.

Their Co-ordinates = (1,0).

From equation (2), we get.

⇒ x - 2y = 4. - - - - - (2).

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

⇒ (0) - 2y = 4.

⇒ - 2y = 4.

⇒ y = - 2.

Their Co-ordinates = (0,-2).

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

⇒ x - 2(0) = 4.

⇒ x - 0 = 4.

⇒ x = 4.

Their Co-ordinates = (4,0).

Area of triangle = 1/2 x Base x Height.

⇒ Base = 4 - 1 = 3.

⇒ Height = -1.8.

Area of triangle = 1/2 x (3) x (-1.8).

Area of triangle = (-5.4)/2 = -2.7 sq. units.

Answer 2

Solution :

$\tt 3x-y=3$

$\sf 3(0) - y =3$

$\tt 0 - y=3$

$\tt -y= 3-0$

$\tt -y=3$

$\tt y =-3$

$\tt 3x-0=3$

$\tt 3x=3$

$\tt x=\dfrac{3}{3}$

$\tt x=1$

$\tt 0-2y=4$

$\tt -2y=4$

$\tt y = \dfrac{4}{-2}$

$\tt y=-2$

$\tt x-0=4$

$\tt x=4$

Area of triangle  = -2.7 sq. units