Use elimination using addition to find the solution

Bell Ringer 3-17 (4 minutes )

1. In order to use elimination with addition, what do you need to have? (15 sec)

2. How is substitution used when doing the elimination method? (45 sec.)

3. p. 362 34 (2.5 min.)

4. Chapter 6 packet #15 (30 sec.)5. HW Real-Life Packet #3 (4 min)

• Elimination using Addition – Must have opposite coefficients – add the 2 equations together.

• Elimination using Subtraction – Must have the same coefficient.

– Subtract the bottom equation from the top by changing all the signs in the bottom equation, then adding.

– Then, add the 2 equations together.

• HW Review – 5 min • Chapter 6 Packet Do Skills Packet 9 - 11

• Midterm Writing Practice

• HW Real Life Packet 4, 8

Multiply Both Equations to Eliminate a Variable

Use elimination to solve the system of equations.2x + y = 233x + 2y = 37

Multiply the first equation by 3 and the second equation by -2 to eliminate x. Distribute, then add the equations.

3(2x + y = 23)

-2(3x + 2y = 37)

– 1y = -5 Add the equations.

-1 = -1

6x + 3y = 69Multiply by 3.

(+) -6x - 4y = -74Multiply by -2

Divide each side by –1.

y = 5Simplify.

Multiply Both Equations to Eliminate a Variable

Now substitute 5 for y in either original equation to find the

value of y.

Answer: The solution is (9, 5).

2x + y = 23 First equation

2x + 5 = 23 y = 5

2x + 5 – 5 = 23 – 5 Subtract 18 from each side.

2x = 18 Simplify.

x = 9Divide by 2 on each side

Cell Phones: Cellular One offers a cell phone plan which the cost is determined by how many minutes and texts used. Within a monthly billing cycle, for every minute used, they charge $0.50 and for every text they charge $0.10. The customer pays $45 with Cellular One. Tee-Mobile’s cell phone plan only charges $0.30 for every minute used and $0.30 per text BUT charges a flat $5.00 usage fee per month. This customer pays $68.00 for their plan.a. Write a system of equations to represent this situation.

Define your variables. American Cellular’s charges: Tee Mobile’s charges: b. What is the solution to the system in this problem?

c. What does the solution represent?