The equations of sides of a triangle are 2x-3y+5=0, 2x+y=7 and 2x+5y=3. Find the coordinates of the vertices.

Vertices A B y C

A ( 2 , 3 )    B ( -1 , 1 )  C ( 3, 1 )

Step-by-step explanation:

We have to solve a two-equation system, by pair of equations as follows

equation (1)   2x - 3y + 5 = 0

equation (2)  2x + y -7    = 0

Solving this system we find let´s say vertex A

0x - 4y +12 = 0      y = 3

Then x ?

2x - 3y + 5 = 0

2x - 9 + 5 = 0     ⇒ 2x = 4     x = 2

Then vertex A ( 2 , 3 )

From equation (1) and (3)

2x - 3y + 5 = 0

2x + 5y - 3 = 0

Agan subtracting (1) - (2)

0x -8y + 8 = 0

y = 1    and      

2x + 5y = 3

2x + 5 = 3

2x = -2

x = -1

Vertex B ( -1 , 1 )

Finally from equation (2) and (3) we get the third vertex C

2x + y - 7 = 0

2x + 5y - 3 = 0

0x -4y -4 = 0

y = 1

2x + y = 7

2x + 1 = 7

2x = 6

x = 3

C ( 3 , 1 )