Lesson 7.3 Solve Linear Systems by Adding or Subtracting Essential Question: How do you solve linear systems by eliminating a variable?

Before we start… Kelly has $1 bills and $5 bills in her wallet and a total of 15 bills. She counts her money and finds she has a total of $47. Write a system of linear equations to model this. How many of each type of bill does Kelly have? Add the equations in your system. Subtract the equations in your system.

Solving Systems Algebraically There are two methods to solving systems algebraically Substitution Elimination It doesn’t matter which method you choose, they will produce the same answer.

The Elimination Method When solving a linear system, you can sometimes add or subtract the equations to obtain a new equation in one variable. Elimination removes one variable from the system so you can easily solve for the variable remaining.

How do you solve by eliminating a variable? Add or subtract the equations to eliminate one variable. Solve the resulting equation for the other variable. Substitute in either original equation to find the value of the eliminated variable. Write your answer as an ordered pair.

Oil Change Two cars get an oil change at the same service center Oil Change Two cars get an oil change at the same service center. Each customer is charged a fee x (in dollars) for the oil change plus y dollars per quart of oil used. The oil change for the car that requires 5 quarts of oil costs $22.45. The oil change for the car that requires 7 quarts of oil costs $25.45. Find the fee and cost per quart of oil.

How do you solve linear systems by eliminating a variable?

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