1. Algebra-2
Section 3-2B

2. Quiz 3-2A: Solve using substitution. 1. 2x + y = -2 -2x + 3y = -82.

3. Vocabulary Elimination Method: Eliminate one of the
variables by adding the two equations together.

4. Vocabulary x – 3y = 5 -x + 5y = 3 2x – 3y = 5 -4x + 3y = 3
Elimination Method: Eliminate one of the
variables by adding the equations together.
What property allows me to
add equations together?
x – 3y = 5
-x + 5y = 3
“same thing left, same thing right”
Adding these equations will eliminate the ‘x’ variable.
2x – 3y = 5
-4x + 3y = 3
Adding these equations will eliminate the ‘y’ variable.

5. Your turn: What variable will be eliminated if I add
the following equations? 1.
2x + y = -2
-2x + 3y = -8 2.
4x – 3 y = -2
-2x + 3y = -8 3.
3x + y = -1
2x + 3y = 18

6. Example x – 3y = 5 -x + 5y = 3 x – x – 3y + 5y = 5 + 3 2y = 8 y = 4
Eliminate one of the variables by adding the equations together.
x – 3y = 5
-x + 5y = 3
x – x – 3y + 5y = 5 + 3
Replace ‘y’ with 4 in
either of the original
equations, then solve
for ‘x’.
2y = 8
y = 4
x – 3(4) = 5
x = 17
Solution: (17, 4)

7. Check the solution: -(17) + 5(4) = 3 (17) – 3(4) = 5 x – 3y = 5
Replace ‘x’ with 17 and ‘y’ with 4 in both of the original equations, to see if the ordered pair (17, 4) is a solution to the system of equations.
x – 3y = 5
-x + 5y = 3
-(17) + 5(4) = 3
(17) – 3(4) = 5
Checks!
Checks!
Solution: (17, 4)

8. Vocabulary 2x – 5y = 6 -x + 5y = 2 2x – x – 5y + 5y = 6 + 2 x = 8
Elimination Method: Eliminate one of the
variables by adding the equations together.
2x – 5y = 6
-x + 5y = 2
2x – x – 5y + 5y = 6 + 2
Replace ‘x’ with 8 in
either of the original
equations, then solve
for ‘y’.
x = 8
-(8) + 5y = 2
5y = 10
Solution: (8, 2)
y = 2

9. Your turn: 2x – y = -2 -2x + 3y = -8 4.
Solve the equation using “elimination”
2x – y = -2
-2x + 3y = -8 4.

10. Your turn: 4x – 3 y = -2 -2x + 3y = -8 5.
Solve the equation using “elimination”
4x – 3 y = -2
-2x + 3y = -8 5.

11. Steps to take to make the equations “addable” (so you can eliminate a variable).
Can you add the two equations together to eliminate the one of the variables?
5x – y = -2
-2x + 3y = -8
(3)5x – (3)y = -2(3)
-2x + 3y = -8
15x – 3y = -6
-2x + 3y = -8

12. Steps to take to make the equations “addable” (so you can eliminate a variable).
Can you add the two equations together to eliminate the one of the variables?
4x + 2y = -1
2x + 3y = 18
4x y = -1
(-2)2x + (-2)3y = 18(-2)
4x + 2y = -1
-4x – 6y = -36

13. Elimination 2x – 2y = 6 -x + 6y = 7 2x – 2y = 6 -x + 6y = 7
What happens if just by adding two equations
One of the variables doesn’t disappear?
Use properties of
Equality: multiply one
Of the equations by a
Number so that the lead
Coefficient is the same
Number but opposite sign
As the other equation.
2x – 2y = 6
-x + 6y = 7
(2)
(2)
2x – 2y = 6
-2x + 12y = 14
10y = 20
y = 2
x = ?

14. Your turn: 3x + y = -1 (-3)3x + (-3)y = -1(-3) 6. 2x + 3y = 18
Solve the equations using “elimination” 6.
3x + y = -1
2x + 3y = 18
(-3)3x + (-3)y = -1(-3)
2x y = 18
-9x – 3y = 3
2x + 3y =18

15. Your turn: 7. 2x + 6y = 2 (-1)2x – (-1)10y = 9(-2) 2x + 6y = 2
Solve using the elimination method: 7.
2x y = 2
(-1)2x – (-1)10y = 9(-2)
2x y = 2
-2x + 10y = -18

16. Your turn: 8. (-2)3x – (-2)4y = -10(-2) 6x + 3y = -42 -6x + 8y = 20
Solve using the elimination method: 8.
(-2)3x – (-2)4y = -10(-2)
6x y = -42
-6x + 8y = 20
6x + 3y = -42

17. Your turn: 9. 3x + 2y = 6 x – 4y = -12 3 (0) + 2y = 6 (0) – 4y = -12
Solution is (0, 3)
5x = 0
x = 0

18. What do you do for this case?
2x + 5y = 14
3x – 2y = -36
Multiply both equations
to get a common coefficient.
(3)2x + (3)5y = 14(3)
(-2)3x – (-2)2y = -36 (-2)
2x + 5(6) = 14
3x – 2(6) = -36
6x + 15y = 42
-6x + 4y = 72
2x + 30 = 14
3x – 12 = -36
2x = -16
3x = -24
19y = 114
y = 6
x = -8
Solution is (-8, 6)

19. Your turn:
Solve using the elimination method:
10.

20. Categories of Solutions:
Ways 2 lines can be graphed:
Cross  one solution
Parallel no solutions
Same line  infinite
number of
solutions

21. How do you know? (1, 0, or infinite #)
Use elimination and both variables disappear and
the resulting equation is either:
a. true:
( 3 = 3 or 0 = 0)
Infinite # of solutions
b. false:
( -2 = 3 or 10 = 0)
No solutions

22. Your turn:
11. Solve using the elimination method:
2x + y = -2
6x + 3y = -8