1. Section 7-3 Solve Systems by Elimination SPI 23D: select the system of equations that could be used to solve a given real-world problem Objective: Solve systems of linear equations by elimination Three Methods of solving Systems of Equations: Solve by Graphing Solve by Substitution Solve by Elimination

2. Solve a System of Linear Equations by Elimination Elimination: Solve systems of equations by using the Properties of Equality (add or subtract equations) Solve the system of linear equations using elimination 6x – 3y = 3 -6x + 5y = 3 1. Add the two equations and eliminate x because the sum of the coefficients is 0. 6x – 3y = 3 -6x + 5y = 3 0 + 2y = 6 2. Solve for the remaining variable by using either equation. y = 3 6x – 3y = 3 6x – 3(3) = 3 6x = 12 x = 2

3. Solve a System of Linear Equations by Elimination Sometimes it is necessary to first, multiply one or both equations by a number to make the coefficients have a sum of zero. Solve the system of linear equations using elimination -2x + 15y = -32 7x – 5y = 17 -2x + 15y = -32 7x – 5y = 17 1. Multiply bottom equation by 3, to make coefficients of y equal 0. -2x + 15y = -32 3(7x – 5y = 17) -2x + 15y = -32 21x – 15y = 51) 2. Subtract to eliminate y.19x = 19 3. Solve for x and substitute into either equation to find y. -2x + 15y = -32-2(1) + 15y = -32 y = -2 x = 1

4. Real-world and Systems of Equations Two groups of students order burritos and tacos at a restaurant. One order of 3 burritos and 4 tacos costs $11.33. The other order of 9 burritos and 5 tacos costs $23.56. Write a system of equations to model the problem. Solve by elimination to find the cost of a burrito and the cost of a taco. 3b + 4t = 11.33 9b + 5t = 23.56 3b + 4t = 11.33 9b + 5t = 23.56 -3(3b + 4t = 11.33) 9b + 5t = 23.56 -9b - 12t = -33.99 9b + 5t = 23.56 -7t = -10.43 t = 1.49 3b + 4(1.49) = 11.33 3b + 5.96 = 11.33 3b = 5.37 b = 1.79 A taco costs $1.49 and a burrito cost $1.79