Question 56846This question is from textbook Glencoe Algebra 2
: Find the coordinates of the vertices of the triangle whose sides are contained in the lines whose equations are 5x - 3y = -7, x + 2y = 9, and 3x - 7y = 1.
5x - 3y = -7
x + 2y = 9 --> x = -2y + 9
3x - 7y = 1
5(-2y + 9) - 3y = -7
-10y + 45 - 3y = -7
-13y + 45 = -7
- 45 on both sides
-13y = -52
divide by -13 on both sides
y = 4
put 4 back into the equation to find x:
5x - 3(4) = -7
5x - 12 = -7
add 12 to both sides:
5x = 5
x = 1
(1, 4)
check answers:
5x - 3y = -7 --> 5(1) - 3(4) = 5 - 12 = -7 (correct)
x + 2y = 9 --> 1 + 2(4) = 1 + 8 = 9 (correct)
3x - 7y = 1 --> 3(1) - 7(4) = 3 - 28 = -25 is not equal to 1. (incorrect)
This question is from textbook Glencoe Algebra 2
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Find the coordinates of the vertices of the triangle whose sides are contained in the lines whose equations are 5x - 3y = -7, x + 2y = 9, and 3x - 7y = 1.
5x - 3y = -7
x + 2y = 9 --> x = -2y + 9
3x - 7y = 1
5(-2y + 9) - 3y = -7
-10y + 45 - 3y = -7
-13y + 45 = -7
- 45 on both sides
-13y = -52
divide by -13 on both sides
y = 4
put 4 back into the equation to find x:
5x - 3(4) = -7
5x - 12 = -7
add 12 to both sides:
5x = 5
x = 1
(1, 4)
check answers:
5x - 3y = -7 --> 5(1) - 3(4) = 5 - 12 = -7 (correct)
x + 2y = 9 --> 1 + 2(4) = 1 + 8 = 9 (correct)
:
You were right about the first vertex, but there are three vertices in a triangle.
Look at the graph:
The red line is: 5x-3y=-7
The green line is: x+2y=9
The blue line is: 3x-7y=1
You found 1, the intersection of:
5x-3y=-7 and x+2y=9
Now you have to find the intersection of:
5x-3y=-7 and 3x-7y=1
Since you know how to do that, I'll just give you and answer to check yourself against. If you don't get that answer, let me know and I'll elaberate: (-2,-1)
Finally you have to find the intersection of:
x+2y=9 and 3x-7y=1 Check your answer against: (5,2).
Let me know, if you need more information. I think you are on the right track and just needed a nudge.
Happy Calculating!!!
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