Staci's Miscellaneous Mayhem
                                             for Algebra 2
 

Using the System of Equations by the   Substitution Method.

Ex:   y = 5-4x
        3x -2y = 12
Before we begin you need to understand that you have already been given a value for "y" and that you will find the "x" by "plugging"  the value into the second equation. 
   Step 1 =   3x-2(5-4x) = 12
   Step 2 =    3x-10+8x = 12
   From here its combining like terms and simple Algebra. 
    Step 3 =   11x-10 = 12
    Step 4 =         +10    +10
    Step 5 =     11x = 22
    Step 6 =     /11     /11
    Step 7 =         x = 2 
    Now that you know the value of "x" you now substitute the "x" value into the first Equation.

 
    SOLVING EQUATIONS USING MULTIPLICATION WITH THE ADDITION METHOD

In this problem you should see that there is a variable that is alone, not proceeded by a number.  Either the “x” or “y” must be canceled. 
5x-2y = 43
x + y = 9 
Step 1: multiply the bottom equation by 2, this will allow you to cancel the “y”. 
5x –2y = 42
( 3x+y ) = 2(9)
5x-2y = 4
6x+2y = 18
You add the x’s , the y’s and the 4 +1811x = 22
Then you divide by 11 , and “x” =2
The 2 is put back into the first equation .5(2)-2y = 4
10-2y = 4
-10 

-2y = -6
/-2    /-2
y = 3

 
Word Problem




   The measure of 1 of 2 supplementary angles is 8 degrees more than 3 times the other.  Find the measure of the larger of the two angles.
Step 1: x = 3y+8           X + Y  = 180          3y+8+y = 180
Step 2: Solve the equation by combining like terms.         3y+8+y = 180 
4y+8 = 180 
 -8      -8 
 4y = 172 
  /4      /4 
y = 43
Step 3: Find the value of the larger angle by “plugging’’ in the value of y.          3(43)+8=137
Step 4: Check the answer of the equation “plugging” the values of x and y  into the original problem. 
137+43 = 180 
*This is a true statement, so we have found the correct answers.   The value of the larger angle   is 137. 
 

 

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