Question

OR
Determine, graphically, the vertices of the triangle formed by the lines represented by 3x - y = 3, 2x - 3y = 2 and x + 2y = 8.
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Answer 1

Answer:

=> 3x-y=3 ------------(1)

=> 2x-3y=2 ----------(2)

=> x+2y=8 ------------(3)

multiply equation (1) by 3 and the subtract equation (2) from it

=> 9x-3y-2x+3y=9-2

=> 7x=7

=> x=1

putting the value of x in (1) we get

3-y=3

y=0

so, one vertex of triangle is (1,0) equation (2) - 2 x equation (3)

=> 2x-3y-2x-4y=2-16

=> -7y= -14

divide both side by 7 , we get

=> y=2

putting the value of y in equation (3) we get

=> x+2y=8

=> x+2*2=8

=> x+4=8

=> x=8-4

=> x=4

The second vertex is (4,2)

2x equation (1)+equation 3 gives

=> 6x-2y+x+2y=6+8

=> 7x=14

dividing both side by 2 we get

=> x=2

putting the value of x in (3) , we get

=> 2+2y=8

=> 2y=8-2

=> 2y=6

=> y=3

the third vertex is (2,3)

We can find the solution is graphically also