1. Systems of Equations What does it mean to substitute something for another? NEXT

2. Combination Plate 1 cheese enchilada 1 beef taco 1 chalupa $6.75 Queso Plate 1 cheese enchilada 1 chile con queso 1 tamale $6.25 Fajita Plate Chicken or beef fajitas 1 chile con queso $7.75 San Antonio Plate 1 quesadilla 1 chile con queso 1 taco $7.50 Los Amigos Plate 2 cheese enchiladas 2 tacos guacamole $7.25 All lunches served with rice and beans. Sorry, no substitutions!

3. Solving without the Cards Using the same two equations: and. NEXT

4. We modeled the equation 3x + 4y = 24. 3x + 4y = 24 NEXT

5. We substituted 2x – 5 for each y in the equation. 2x – 5 3x + 4y = 24 3x + 4(2x – 5) = 24 NEXT

6. 2x – 5 We simplified the left side of the equation. 3 xs plus 4 sets of 2x 3x + 4(2x) 3x + 8x 11x 4 sets of –5 4(–5) –20 AND 11x – 20 = 24 3x + 4y = 24 3x + 4(2x – 5) = 24 3x + 8x – 20 = 24 11x – 20 = 24 NEXT

7. We solved the equation to determine the value of x. NEXT

8. We returned to the original model of 3x + 4y = 24. 3x + 4y = 24 NEXT

9. 3x + 4y = 24 We substituted 4 in place of each x in the equation. 4 4 4 3(4) + 4y = 24 NEXT

10. 3x + 4y = 24 4 4 4 3(4) + 4y = 24 NEXT We simplified the left side of the equation. 4 y’s 4y 3 sets of 4 3(4) 12 AND 12 + 4y = 24

11. We solved the equation to determine the value of y. NEXT

12. What is the solution? The solution to the system of equations is What does this mean? NEXT

13. Solve the system by graphing. NEXT The values x = 4 and y = 3 satisfy both equations.

14. Substitute the expression that is equal to the circled variable in the other equation. Solve an equation for one variable. Simplify and solve. Substitute the value found into the equation that was solved for the circled variable. Simplify and solve. Write the solution. yes no Notes Is one equation solved for one of the variables? Circle the isolated variable.