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METHODS FOR SOLVING SYSTEMS OF EQUATIONS (Substitution Method ((12-6y-2y=4…
METHODS FOR SOLVING SYSTEMS OF EQUATIONS
Substitution Method
When there is one y or x= equation and another equation that is not y or x= you substitute the y or x= equation in for the other value.
x = 4 − 2y
3x − 2y = 4
3(4-2y)-2y=4
12-6y-2y=4
12-8y=4
-8y=-8
y=1
Equal values method
use this method if you see y= or x= in both equations
Example:
x = −5y + 2
x = 3y − 2
to solve this set the equations equal to each other -5y+2=3y-2
solve the equation
y = 1/2x+ 4
y = −2x + 9
to solve set the equations equal to each other y+3=-4y-6
solve the equation
Elimination Method
Addition
What is it?
The elimination method is the process of eliminating variables that mean can make a problem easier to solve
Example
y=-2
Then move on to the top equation and add the Y value and solve to get the value of X
x+3(-2)=-5
x+-6=-5
x=1
Subtraction
What is it?
Turning all of the numbers on one side negative so that you can eliminate them.
Example: 3x + y = 1
4x + y = 2
Linear Combinations
What is it?
you take one equation and you multiply the entire equation by a number to have an equal value in both equations and you eliminate them and combine both equations and solve.
Example
3x+2y=1
x+4y=2
By: Fiona, Casey, Anna, and Dylan
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