Name: ____________________________________
Date: _________________________________
Substitution and Elimination Method Notes & Worksheet
SUBSTITUTION METHOD: Remember, when using the substitution method, one of
your variables must be given to you.
Example:
y = 8+1
x + y = 120
Plug the 8 +1 into the y spot in your second equation.
x + (8 +1 ) = 120
x + 9 = 120
x + 9 – 9 = 120 – 9
x + 0 = 111
x
= 111
Now that you have your x (111) substitute it into the x spot.
111 + y = 120
110 – 110 + y = 120 – 110
0+y=9
y=9
ELIMINATION METHOD: Remember, with the elimination method you add both
constraints together. However, before doing so, you must make sure that one of
your variables cancels out. Whatever you did to cancel/eliminate the variable
you must do to the rest of your equation.
Example:
2x + 3y = 6
x + 5y = 10
In this case you want to eliminate you x so that you can solve for your y. Therefore
you need to think, what can I do to my x that when I add it to 2x it will give me zero.
2x + 3y = 6
+ x + 5y = 10 * notice here I must multiply my x by (-2) to eliminate my x.
2x + 3y = 6
+ (-2) + (-10) = (-20) * because I multiplied my x by (-2) I must multiply everything else by (-2).
Now that I have eliminated one of my variables I can add them.
2x + 3y = 6
+ (-2) + (-10y) = (-20)
0 - 7y = - 14
- 7y = - 14
-7
-7
y = 2
2x + 3(2) = 6
2x + 6 = 6
2x + 6- 6 = 6-6
2x = 0
2
2
x = 0
Task: Use either the substitution or elimination method to find the x and y
coordinates. Make sure to tell me which method you used. Show all your work!
1.
x=
2.
x=
3.
x=
4.
x=
5.
x=
y = 25
x + y = 200
y=
3x + y = 9
y=
2x + 3y = 20
y=
y = 2x +4
y=
4x + y = 24
y=
I used the ______________________ method.
5x + 4y = 22
I used the ______________________ method.
x+ y=4
I used the ______________________ method.
3x + y = 9
I used the ______________________ method.
2x -3y = -2
I used the ______________________ method.