1. Section 3: solving Systems of Equations with combinations/elimination
Homework: Pg 142 #49-55, 76, 85
Section 3: solving Systems of Equations with combinations/elimination
Learning Target: I will solve systems of equations in real-world and mathematical situations using elimination.

2. Review
When is it easiest to solve a system of equations using the graphing method?
When is it easiest to solve a system of equations using the substitution method?

3. Solve the System by Graphing
y = 5x – 4 y = 2x - 1

4. Solve the System using Substitution
x = 2y x + 5y = 6

5. Elimination/Combination
Elimination/Combination is best used when both equations in the system are in standard form (Ax + By = C)
This method combines both equations by adding them together, but one of the variables must be eliminated as soon as the equations are combined.

6. Ex 1: Solve using Elimination/Combinations
4x – 2y = 7 * Are the equations in standard form? x + 2y = 3

7. EX 2: Solve the System
2x – 3y = 6 -2x + 3y = -6
If 3x – 4y =12, can you write another equation to make the system no solutions?
If 3x – 4y =12, can you write another equation to make the system no solutions?

8. Ex 3: Elimination/Combination
Solve the system. 2x – 3y = 10 4x + 6y = 8

9. Ex 4 – Solve with Elimination
Joey and Erik go to a carnival. Joey rides the Ferris wheel 6 times and the Tilt-a-Whirl twice. Erik rides the Ferris wheel 9 times but gets sick on the Tilt-a-Whirl so he only rides it once. Joey’s fun cost $2.50 and Erik’s fun cost $ How much is a ride on the Tilt-a-Whirl?

10. Ex 5: Forcing an Elimination
A. 4x + 9y = 2 B. -5x + 8y = 16 2x – 5y = 6 12x + 24y = 15

11. Ex 6: May the Force be with you!
3x + 7y = 15
5x + 2y = -4

12. HOMEWORK Pg 142 #49-55, 76, 85 Type equation here.Answers:
49. a) x + y = 13
4x + 2y = 38
b) 6 doubles, 7 singles
(3, 3)
(0, 4)
(-5, -4)
Many Solutions
(-5, -3)
(8, -6)
Gloria is correct: see explanation
a) 10x + 15y ≥ 350
b) see graph
c) no