Question

Solve the equations graphically
2x+y=2
2y-x=4
Also find the area of the triangle formed by two lines and the line y=0

Answer 1

Answer:

Area of triangle is 5 square unit.

Step-by-step explanation:

Given : Equation 1 - $2x+y=2$

Equation 2 - $2y-x=4$

Equation 3- $y=0$

Solve the equation graphically and find the area of the triangle formed.

Solution : The solution graphically is attached in which equation 1,2 and 3 form the triangle by points (0,2),(-4,0),(1,0) and shaded region represent the triangle formed.

Now, to find area of triangle we need base and height.

From graphically we see that the height of triangle is (0,2)=2 unit and base is (1-(-4))=5 unit.

Area of triangle $A= \frac{1}{2}\times b\times h$

where b is the base and h is the height,

$A= \frac{1}{2}\times 5\times 2= 5 unit^2$

Therefore, Area of triangle is 5 square unit.

Answer 2

Given  : 2x+y=2 , 2y-x=4.

To Find :   the area of a triangle formed by the two lines and the line y=0

Solution:

2x+y=2

2y-x=4

y = 0

2x+y=2 , y = 0

=> point of intersection  ( 1 ,  0)

2y-x=4  , y = 0

=> point of intersection  ( -4 ,  0)

2x+y=2 , 2y-x=4

=>  point of intersection  ( 0 , 2)

Triangle is formed with base = ( 1 - (-4)  = 5

Height = 2

Area of Triangle = (1/2) * base * height

= (1/2) * 5 * 2

= 5 sq units

or area of triangles by vertex    ( 1 ,  0)  , ( -4 ,  0)  and   ( 0 , 2)

= (1/2) | 1 ( 0 - 2) - 4( 2 - 0)  + 0 (0 - 0) |

= (1/2) |  - 2 - 8 |

= (1/2) | - 10 |

= (1/2) (10)

= 5 sq units

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