Alicia's Algebra 

I did this website for a grade in my Algebra 2 class.
It is to help other students understand the systems of equations!
I really enjoyed doing this, and I hope it helps you.


Substitution Problem
3x - 4y = -15
5x + y = -2 ---> y = -5x-2
3x - 4 (-5x-2) = -15
3x + 20x + 8 = -15
23x = -23
23x/23 = -23/23
x = -1

y = -5(-1) - 2
y = 5 - 2
y = 3

 The answer is  (-1 , 3)
* I solved the equation 5x + y = -2 for "y", because y had only a coefficient of one.
*After I solved for "y", I plugged that equation into 3x - 4y = -15, and then I solved that one for "x".
* x = 1, so I plugged that into the equation y = -5x - 2.

*  So the answer ended up being x = -1 and y =  3.

 
      Linear Combination
-----------------------------------------------------
  7x - 3y = -5
  3x + 2y = 11 
  10x - y = 6 -------> y = 10x - 6

  7x - 3(10x - 6)
  7x - 30x + 18 = -5
    -23x/-23 = -23/-23
    x = 1

   y = 10(1) - 6
   y = 4

   ans. = (1,4)
 
 *  First, I put the two equations on top of each other and added then together.
* The equation ended up being 10x - y = 6, then I solved for "y", so the equation is y=10x-6.
*  I then plugged that equation into 7x - 3x = -5. 
* That ended up being x = 1.
*  I plugged x into the equation of "y", so y = 4.
* The answer ended up being
x = 1, and y = 4..

Word Problem
One day a store sold 30 sunglasses.  The circle frames cost $9.95.  The square frames cost $10.50. In all. $310.60 worth of sunglasses were sold. How many of each kind were sold?

x = cost of circle frames
y = cost of square frames.
9.95x + 10.50y = 310.60
- 9.95                        -9.95

 x + y = 30
x = -y + 30
9.95 (-y + 30) +10.5y=310.6

-9.95y +298.5+10.5y=310.6
.55y = 12.1
y = 22 (square)

9.95x + 231 = 310.6
9.95x = 79.6
x = 8 (circle)

 *I made two equations from "x" equaling the cost of circle frames *
 
*"y" equaling the cost of square frames.

*I solved the first equation for x. 

*After I solved that, I plugged it in the original equation and got what y equals. 

*So I plugged what y equaled into the equation of x and then I got the answer. 

*x= 8 circle frames and y = 22 square frames.



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