SOLUTION: 21. Given: Ray ST bisects Angle(<) RSV m< RST= x+y m< TSV= 2x-2y m< RSV= 64 degrees Find: x and y It also gives a diagram before it which

Question 85400: 21. Given: Ray ST bisects Angle(<) RSV
m< RST= x+y
m< TSV= 2x-2y
m< RSV= 64 degrees
Find: x and y
It also gives a diagram before it which i will try and describe:
It is a pic of an angle split in two. the vertex is named s and the top ray has the endpoint called r and the middle endpoint it t and the bottom endpoint is v. I have tried to explain the diagram but i don't think i did it very well. oh, well.
if you go to this picture site and it has the picture but just different names for the points: http://education.yahoo.com/homework_help/math_help/solutionimages/minigeogt/1/1/1/minigeogt_1_1_1_13_1/f-37-49-oyo-1.gif
I'm sorry if you are asking what in the world is she talking about because it is understandable!
thank you if you find the answer!
-Athena
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since m< RST and m< TSV are half of m< RSV, we know this expression is true:

Also, since m< RST= x+y and m< TSV= 2x-2y, we can set up the following system of equations:

Now we can solve for x and y by addition/elimination:

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition

Lets start with the given system of linear equations

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 1 and 2 to some equal number, we could try to get them to the LCM.

Since the LCM of 1 and 2 is 2, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -1 like this:

Multiply the top equation (both sides) by 2
Multiply the bottom equation (both sides) by -1

So after multiplying we get this:

Notice how 2 and -2 add to zero (ie )

Now add the equations together. In order to add 2 equations, group like terms and combine them

Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.

So after adding and canceling out the x terms we're left with:

Divide both sides by to solve for y

Reduce

Now plug this answer into the top equation to solve for x

Plug in

Multiply

Subtract from both sides

Combine the terms on the right side

Multiply both sides by . This will cancel out on the left side.

Multiply the terms on the right side

So our answer is

,

which also looks like

(, )

Notice if we graph the equations (if you need help with graphing, check out this solver)

we get

graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).

and we can see that the two equations intersect at (,). This verifies our answer.

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