Question

Determine algebraically, the vertices of the triangle formed by the lines 5x - y = 5, x + 2y = 1, 6x + y = 7.

Answer 1

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)x6
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)