3.2 – Solving Systems Algebraically

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September 11, 2014 Page 18 – 19 in Notes

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Presentation transcript:

3.2 – Solving Systems Algebraically

The goal of substitution is to put on equation into the other so there is only one variable to solve for. Substitution

Steps for Substitution Solve 1 of the equations for 1 of its variables Substitute the expression from Step 1 into the other equation and solve. Substitute the value from Step 2 into an equation and solve for the remaining variable. Steps for Substitution

Example: Solve the linear system. 3x – y = 13 2x + 2y = -10

-x + 3y = 1 4x + 6y = 10

The goal with linear combination is to get one variable to cancel. Then you will only have 1 equation with 1 unknown and you can solve for it. Linear Combination

What would you have to add to the following terms for their sum to be zero? 3x -2y -x 10y Think Opposite!

Think Opposite! 3x, x -4y, 2y 5x, 3x 2 terms are given below. Find what you could multiply one (or two) term(s) by so that the sum of the two terms is zero. 3x, x -4y, 2y 5x, 3x Think Opposite!

Steps to Solve by Linear Combination Make sure all like terms are lined up. Multiply one or both equations by a constant so 1 variable will cancel when the 2 equations are added. Add the two equations together and solve. Substitute answer into an original equation to find the other variable.

Solve the following linear systems. 1. 2x – 6y = 19 -3x + 2y = 10

2. 3x + 2y = 10 5x - 7y = -4

3. 6x – 4y = 14 -3x + 2y = 7

4. 9x – 3y = 15 -3x + y = -5

Suppose you are going on vacation and leaving your dog in a kennel Suppose you are going on vacation and leaving your dog in a kennel. The Bowowery charges $25 per day, which includes a one-time grooming treatment. The Poochpad charges $20 per day and a one-time fee of $30 for grooming. Write a system of equations to represent the cost, c, for d days that your dog will stay at the kennel. Find the number of days for which the costs are the same. If your vacation is a week long, which kennel should you choose? Explain

You and your business partner are mailing advertising flyers to your customers. You address 6 flyers each minute and have already done 80. Your partner addresses 4 flyers each minute and has already done 100. Write a system of equations and find when you will have addressed the same number of flyers.