SOLUTION: I am working on systems of linear equations, which I have until now been able to complete by using substitution or elimination methods. Now, however, my homework requires me to so

Question 58323: I am working on systems of linear equations, which I have until now been able to complete by using substitution or elimination methods. Now, however, my homework requires me to solve systems with more than two equations. This problem has three equations, each representing a side of a triangle, and is asking for the three coordinates for the vertices.
I founnd the points at which the first line intersects with the other two (seperately), but do not know how to determine the third vertex.
HERE ARE THE EQUATIONS:
x-y=7
3x-11y=-1
x+y+1=0
AND HERE IS MY WORK THUS FAR:
x-y=7
x=7+y

3(7+y)-11y=-1
21+3y-11y=-1
21-8y=-1
-8y=-22
y=2.75
3x-11(2.75)=-1
3x-30.25=-1
3x=29.25
x=9.75
the point for this vertex is (9.75, 2.75)

7+y+y+1=0
8+2y=0
2y=-8
y=-4
x+-4+1=0
x-3=0
x=3
the point for this vertex is (3,-4)
**so i was able to find these two vertices by substitution method, but do not know how to determine the third one. If any tutor could work on this and send me a solution ASAP, so that I am able to complete the rest of the problems, I would greatly appreciate it!!
With much gratitude and thanks,
A STUDENT
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Dear A Student,
L1) x-y=7
L2) 3x-11y=-1
L3) x+y+1=0
You found the intersection of L1 and L2 (9.75,2.75)
You found the intersection of L1 and L3 (3,-4)
Now you have to find the intersection of L2 and L3:
3x-11y=-1
x+y+1=0--->x=-y-1
:
3(-y-1)-11y=-1
-3y-3-11y=-1
-14y-3=-1
-14y=2

The third vertex is (-6/7,-1/7)
It helps to graph the lines so you can see which lines you need to use for each vertex.
Happy Calculating!!!

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