Question

determine algebraically, the vertices of the triangle formed by the lines 5x-y=5,x+2y=1 and 6x+y=17

Answer 1

We will deal with two lines at a time and solve them simultaneously:

L1: 5x-y=5

L2: x+2y=1

L3: 6x+y=17

L1 and L2

5x-y=5

(x+2y=1) x5

5x+10y=5

5x-y=5

11y=0

y=0

x=1

point (1, 0)

L1 and L3

5x-y=5

6x+y=17

Add

11x = 2

X =2

Y= 5

Point (2, 5 )

L2 and L3

(x+2y=1) x 6

6x+y=17

6x+12y=6

6x+y=17

11y= - 11

y= - 1

x = 3

Point (3, -1)

The vertices of the triangle formed are:

(1, 0), (2, 5 ), (3, -1)