Question

find the area of the triangle formed by the lines x+y=6,x-3y=2,5x-3y+2=0

Answer 1

eq 1-

   x+y=6.....(1)

 

eq 2-   x-3y=2....(2)

 

eq 3-   5x-3y+2=0.....(3)

 

By (1) and (2)

Subtracting (2) from (1

)

4y=4

y=1

x=5

 

By (2) and (3) 

Subtracting (2) from (3

)


 

4x=4

x=-1

y=-3

By (3) and (1) 

Multiply(1) by 3 and adding(3)

 

8x=16

x=2

y=4

 

coordinates

 

of points of triangle

 

are (5,1),(-1,-3),(2,4)

 

Area of triangle

 

=|5(-3-4)-1(4-1)+2(1-(-3))|/2

 

=15


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Answer 2

Here is a graph hope it helps

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