Do Now 12/10/18

1. Do Now 12/10/18 • Copy HW in your planner. • Text p. 239, #4-22 evens, 27 & 28 • With your partner, complete Exploration 1 & 2 on pages 132 & 133 in your Student Journal.

2. Essential QuestionHow can you solve a system of linear equations? • With your partner, complete Exploration 1 & 2 on pages 132 & 133 in your Student Journal.

3. Essential QuestionHow can you solve a system of linear equations?

4. Essential QuestionHow can you solve a system of linear equations?

5. Essential QuestionHow can you solve a system of linear equations?

6. Chapter 5 Preview “Solving Systems of Linear Equations” (5.1) Solving Systems of Linear Equations by Graphing (5.2) Solve Systems of Linear Equations by Substitution (5.3) Solve Systems of Linear Equations by Elimination (5.4) Solve Special Systems of Linear Equations (5.6) Graphing Linear Inequalities in Two Variables • (5.7) Systems of Linear Inequalities

7. Section 5.1“Solving Systems of Linear Equations by Graphing” Linear System– consists of two or more linear equations. x + 2y = 7 Equation 1 3x – 2y = 5 Equation 2 A solution to a linear system is an ordered pair (a point) where the two linear equations (lines) intersect (cross).

8. 7 = 7 5 3(3)–2(2) 5 = 5 ? ? = = 3+ 2(2) 7 Using a Graph to Solve a Linear System Use the graph to solve the system. Then check your solution algebraically. Equation 1 x + 2y = 7 Equation2 3x – 2y = 5 SOLUTION The lines appear to intersect at the point (3, 2). CHECK Substitute3forxand2foryin each equation. Equation 1 Equation2 Because the ordered pair (3, 2) is a solution of each equation, it is a solution of the system. x+2y=7 3x–2y=5

9. -7 -4+(-3) -7= -7 ? ? = = 4+ 4(-3) -8 Using a Graph to Solve a Linear System Use the graph to solve the system. Then check your solution algebraically. Equation 1 x + 4y = -8 Equation2 -x +y = -7 SOLUTION The lines appear to intersect at the point (4, -3). CHECK Substitute 4 forxand -3 foryin each equation. Equation 1 Equation2 Because the ordered pair (4, -3) is a solution of each equation, it is a solution of the system. x+4y=-8 -x+y=-7 -8 = -8

11. Solve the System by Graphing Because the ordered pair (2, 0) is a solution of each equation, it is a solution of the system. y-axis 5 4 3 2 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x-axis Substitute2forxand0foryin each equation. -1 -2 -3 -4 -5

12. On Your Own

13. Solve the system by graphing. Use a graphing calculator. y = -0.5x + 10 4x – y = 1.5 2x + y = 1.5 y = x – 5

14. A B y = 4x y = 4x y = 90 + 13x y = 13x D C y = 13x y = 90 + 4x y = 90 + 4x y = 90 + 13x Standardized Test Practice The parks and recreation department in your town offers a season pass for $90. As a season pass holder, you pay $4 per session to use the town’s tennis courts. Without the season pass, you pay $13 per session to use the tennis courts. Which system of equations can be used to find the number xof sessions of tennis after which the total cost ywith a season pass, including the cost of the pass, is the same as the total cost without a season pass?

15. y = 90+ 4x A B y = 4x y = 4x y = 90 + 13x y = 13x y=13x D C y = 13x y = 90 + 4x y = 90 + 4x y = 90 + 13x Standardized Test Practice Which system of equations can be used to find the number xof sessions of tennis after which the total cost ywith a season pass, including the cost of the pass, is the same as the total cost without a season pass? EQUATION1 EQUATION2

16. Solve a multi-step problem A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented. STEP1 Write a linear system. Let xbe the number of pairs of skates rented, and let ybe the number of bicycles rented. x + y =25 Equation for number of rentals 15x + 30y = 450 Equation for money collected from rentals

17. ANSWER The business rented 20 pairs of skates and 5 bicycles. ? ? 15(20)+30(5) 450 20+525 = = 450 =450 25 =25 Solve a multi-step problem STEP2 Graph both equations. STEP3 Estimate the point of intersection. The two lines appear to intersect at(20, 5). STEP4 Check whether (20, 5) is a solution.

18. Homework • Text p. 239, #4-22 evens, 27 & 28