SOLUTION: Linear Systems 3. The arms of an angle lie on the lines x+4y=9 and 3x-2y=13. What are the coordinates of the vertex of the angle? pleaseeeeeeeeeeeeeeeee Thank you very much

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Question 180765: Linear Systems
3. The arms of an angle lie on the lines x+4y=9 and 3x-2y=13. What are the coordinates of the vertex of the angle?
pleaseeeeeeeeeeeeeeeee
Thank you very much
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28x%2B4y=9%2C3x-2y=13%29


2%283x-2y%29=2%2813%29 Multiply the both sides of the second equation by 2.


6x-4y=26 Distribute and multiply.


So we have the new system of equations:
system%28x%2B4y=9%2C6x-4y=26%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2B4y%29%2B%286x-4y%29=%289%29%2B%2826%29


%281x%2B6x%29%2B%284y%2B-4y%29=9%2B26 Group like terms.


7x%2B0y=35 Combine like terms.


7x=35 Simplify.


x=%2835%29%2F%287%29 Divide both sides by 7 to isolate x.


x=5 Reduce.


------------------------------------------------------------------


x%2B4y=9 Now go back to the first equation.


5%2B4y=9 Plug in x=5.


5%2B4y=9 Multiply.


4y=9-5 Subtract 5 from both sides.


4y=4 Combine like terms on the right side.


y=%284%29%2F%284%29 Divide both sides by 4 to isolate y.


y=1 Reduce.


So our answer is x=5 and y=1.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of x%2B4y=9 (red) and 3x-2y=13 (green)



So from the graph, we see that the vertex of the angle is the point