Section 3: solving Systems of Equations with combinations/elimination

SECTION 3: SOLVING SYSTEMS OF EQUATIONS

WITH COMBINATIONS/ELIMINATION

Homework: Pg 142 #49-55, 76, 85

Learning Target: I will solve systems of equations in real-world and mathematical situations using elimination.

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?

Solve the System by Graphing

y = 5x – 4y = 2x - 1

Solve the System using Substitution

x = 2y + 3-4x + 5y = 6

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.

Ex 1: Solve using Elimination/Combinations

4x – 2y = 7 * Are the equations in standard form?

x + 2y = 3

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?

Ex 3: Elimination/Combination

Solve the system.2x – 3y = 104x + 6y = 8

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 $2.75. How much is a ride on the Tilt-a-Whirl?

Ex 5: Forcing an Elimination

A. 4x + 9y = 2 B. -5x + 8y = 16 2x – 5y = 6 12x + 24y = 15

Ex 6: May the Force be with you!

3x + 7y = 15 5x + 2y = -4

HOMEWORK

Pg 142 #49-55, 76, 85Answers:49. a) x + y = 13 4x + 2y = 38 b) 6 doubles, 7 singles50.(3, 3)51. (0, 4)52. (-5, -4)53. Many Solutions54. (-5, -3)55. (8, -6)76.Gloria is correct: see explanation85.a) 10x + 15y ≥ 350 b) see graph c) no