Question

raw the graph of 2x + 3y = 12 and 2y –1 = x on a graph paper, shaded the region between lines and x-axis. Also, find the area of shaded region

Answer 1

EXPLANATION.

Graph of the equation.

⇒ 2x + 3y = 12. - - - - - (1).

⇒ 2y - 1 = x. - - - - - (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.

⇒ 2y - 1 = x. - - - - - (2).

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

⇒ 2y - 1 = (0).

⇒ 2y - 1 = 0.

⇒ 2y = 1.

⇒ y = 1/2.

⇒ y = 0.5.

Their Co-ordinates = (0,0.5).

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

⇒ 2(0) - 1 = x.

⇒ - 1 = x.

⇒ x = - 1.

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

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

As we know that,

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

⇒ Base = 6 - (-1) = 7 cm.

⇒ Height = 2 cm.

Area of triangle = 1/2 x 7 x 2.

Area of triangle = 7 sq. units.

Answer 2

Answer:

$\underline{\purple{\ddot{\MasterRohith}}}$

Given:-

• Graph of the equations
• 2x+3y= 12
• 2y-1=x

To find :-

• Plotting the graph and
• Finding area of triangle.

Explanation :-

Here given two graph solutions

• 1)2x+3y=12 (i)
• 2)2x-1=x (ii)

• FROM THE EQUATION 1 WE GET

• 2x+3y=12

• Here putting the value of x = 0 in equation
• 2 (0)+3y=12
• 0 +3y=12
• y =12/3
• y = 4.

Their coordinates is =(0,4)

Now putting the value of y=0 in equation we get that,

• 2x+3 (0)=12
• 2x + 0 =12
• 2x =12
• x =12/2
• x =6.

Their coordinates is =(0,6).

• From equation 2 we get,

Putting x =0 in equation 2 we get,

• 2y-1=x
• 2y-1=(0)
• 2y =1
• y=1/2

Their coordinates is=(0,0.5)

• Putting the value of y=0 in equation ii) we get
• 2y-1=x
• 2(0)-1=x
• 0-1=x
• -1=x

Their coordinates is =(1,0).

Both these curves are intersect at a point of =(3,2)

• At the last we should find area of triangle

• Area of triangle =1/2×base×height
• Here ,
• Base=6-(-1)=7
• Height=2cm
• Area of triangle =1/2×7×2
• Area of triangle =7sq.units.

Hope it helps u mate .

Thank you .