The graphs y - 2x = 1, 4x + y = 7, and 2y - x = -4 contain the sides of a triangle.  Find the coordinates of the vertices of the triangle.

steveschoen | Certified Educator

To do this, you would be solving a 2 by 2 system of equation.  You can make 3 of these systems from the equations above.  So, for one system:

y - 2x = 1    --> y = 2x + 1

4x + y = 7   --> 4x + (2x+1) = 7

6x + 1 = 7

6x = 6

x = 1

Plugging this back into either original equation:

y = 2*1 + 1 = 3

So, one vertex is (1,3)

Another system of equations:

y - 2x = 1   --> y = 2x + 1

2y - x = 4  --> 2(2x+1) - x = -4

4x + 2 - x = -4

3x + 2 = -4

3x = -6

x = -2

Plugging this back into one of the original equations:

y -2(-2) = 1

y + 4 = 1

y = -3

So, another vertex is (-2,-3)

For the last vertex, solve this system:

4x + y = 7   -->   y = -4x + 7

2y - x = -4   -->    2(-4x+7) - x = -4

-8x + 14 - x = -4

-9x + 14 = -4

-9x = -18

x = 2

Plugging this back into one of the original equations:

4*2 + y = 7

8 + y = 7

y = -1

So, the last vertex is (2,-1)