Ch. 7 - Systems of Linear Equations - Block A fileStandard form: Ax By C Linear equations do NOT have to be written in one of the above forms. All linear equations, regardless of which

Foundations of Mathematics & Pre-Calculus 10 Chapter 7 – Systems of Linear Equations

Created by Ms. Lee 1 of 17 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson

First Name: ________________________ Last Name: ________________________ Block: ______

Ch. 7 – Systems of Linear Equations

7.1 – SYSTEMS OF LINEAR EQUATIONS 2

Ch. 7.1 HW: p. 401 #4 – 6 4

7.2 – SOLVING SYSTEMS OF EQUATIONS BY GRAPHING 4

Ch. 7. 2 HW: p. 409 #3 – 5, 7a, 8 6

7.4 – USING A SUBSTITUTION STRATEGY TO SOLVE SYSTEMS OF EQUATIONS 6

Ch. 7. 4 HW: p. 425 #4, 5 10

7.5 – USING AN ELIMINATION STRATEGY TO SOLVE SYSTEMS OF EQUATIONS 11

Ch. 7. 5 HW: p. 437#3, 5, 6, 8, 12 14

7.6 – PROPERTIES OF SYSTEMS OF LINEAR EQUATIONS 15

Ch. 7. 6 HW: p. 448 #4, 5, 7 16

CHAPTER 7 ‐ REVIEW 17

HW: p.452 #10, 15, p.455 #2, 5 17



7.1–SystemsofLinearEquations Identifying Linear equations: We’ve looked at several forms of linear equations:

Slope-intercept bmxy

Slope-point form: )( 11 xxmyy

General form: 0 CByAx

Standard form: CByAx Linear equations do NOT have to be written in one of the above forms. All linear equations, regardless of which form it’s written in, can always be transformed into the general form; 0 CByAx Examples: Equations Linear Equation? (yes/no) If yes, write the equation in 0 CByAx

13 xy

32 yx

3y

3 xy

yx 12

3

)2(2

31 xy

32 yx

042 x

yx

21



Definitions: A system of linear equations is made up of _______________________ linear equations Solution to a linear system (in two variables) is any ordered pairs (x, y) that satisfy _______

equations. Examples: 1) Determine if (1, 2) is a solution to the following linear system.

13 yx 0125 yx

2) Determine if (-1, 3) is a solution to the following linear system.

yx 14 3 yx

3) Determine if (-1, 4) is a solution to the following linear system. 242 yx

yx 73

4) Determine if (-3, -1) is a solution to the following linear system.

12 yx 52 yx



5) A school raised $140 by collecting 2000 cans and glass bottles for recycling. The school received 5 ¢ for a can and 10 ¢ for a bottle.

a) Create a linear system to model this situation.

b) Did school collect 1200 cans and 800 bottles?

Ch. 7.1 HW: p. 401 #4 – 6

7.2–SolvingSystemsofEquationsbyGraphingRecap:

A system of linear equations is made up of _______________________ linear equations Solution to a linear system (in two variables) is any ordered pairs (x, y) that satisfy _______

equations. There are several ways to solve linear systems:



Examples 1) Solve the following linear system graphically.

a) x – y = -2 4x + 2y = 16

b) 2y – 3x = -2 3y + x = -3

c) 332 yx 4 yx

d) 033 yx 32 yx

You try: 1) Solve the linear system.

13

1555

yx

yx

02435

63

yx

yx



2) One plane left Regina at noon to travel 1400 mi. to Ottawa at an average speed of 400 mph. Another plane left Ottawa at the same time to travel to Regina at an average speed of 350 mph. A linear system that models this situation is:

tD 4001400 tD 350

where D is the distance in miles from Ottawa and t is the time in hours since the planes took off. a) Graph the linear system above.

b) Use the graph to solve this problem: When do the planes pass each other and how far are they

from Ottawa?

Ch. 7. 2 HW: p. 409 #3 – 5, 7a, 8

7.4–UsingaSubstitutionStrategytoSolveSystemsofEquations Recap:

A system of linear equations is made up of _______________________ linear equations Solution to a linear system (in two variables) is any ordered pairs (x, y) that satisfy _______

equations. There are several ways to solve linear systems:

By graphing By using substitution method By using elimination method



Examples: 1. Given the linear system below, solve by substitution.

52 yx y = 3

Substitute ____ into ____ in equation _____.

Graph and check.

2. Given the linear system below, solve by substitution.

632 yx x = 2 Substitute ____ into ____ in equation _____.

Graph and check.

3. Given the linear system below, solve by substitution.

63 yx y = x2

Substitute ____ into ____ in equation _____.

Graph and check.



4. Given the linear system below 83 yx 1835 yx

a) Solve this linear system by substitution. Step 1: Pick an equation and isolate one of the variables (whichever is easiest to isolate). Step2: Substitute ______ into ____ in equation ___ Step 4: Substitute _____ into ____ in equation ____

b) Graph the system to see if the solution makes sense.

5. Given the linear system below

742 yx 54 yx

Solve this linear system by substitution.

Verify ________ is the solution to the linear system.



6. Given the linear system below 532 yx

82 yx Solve this linear system by substitution.

Verify ________ is the solution to the linear system.

You try: 1. Solve each system

a) 9 yx

xy 2

b) 102 yx

yx 2



2. Solve each system a)

1132 yx 155 yx

b) 7 yx

102 yx

3. Solve each system

a) 463 yx

12 yx

b) 82 yx 535 yx

Ch. 7. 4 HW: p. 425 #4, 5



7.5–UsinganEliminationStrategytoSolveSystemsofEquations Goal: To eliminate one of the variables by adding or subtracting the equations. In some cases you need to multiply one or both equations first. Examples: 7. Solve the linear system below by using Elimination method (by addition).

a) b) 532 yx 1033 yx

142 yx 562 yx

8. Solve the linear system below by using Elimination method (by subtraction).

a) b) 832 yx 633 yx

1132 yx 1662 yx



9. Solve the linear system below by using Elimination method. (Multiply and then Add/Subract) a) b)

52 yx 457 yx

523 yx 54 yx

c) d)

158 nm 046 nm

354 yx 173 yx



10. Solve the linear system involving fractions by using Elimination method. (Get rid of fractions first) a) b)

82

15 yx

1664 yx

145

26 yx

62

1

3

1 yx

You try 4. Solve each system

b) 1832 yx

632 yx

b) 125 yx

745 yx



5. Solve each system a)

33 yx 532 yx

b) 16103 yx 624 yx

6. Solve each system

a) 3838 yx 2654 yx

b) 573 dc

2254 dc

Ch. 7. 5 HW: p. 437#3, 5, 6, 8, 12



7.6–PropertiesofSystemsofLinearEquationsGraph the system to solve: Solutions: Use elimination method to solve: 1) 3x + y = 9 6x + 2y = 6

2) x + 3y = 6 2x + 6y = 12

3) x + 2y = 4 -x + y = -1



Conclusion: In order to determine possible solutions for a linear system, you can re-write the equations in the slope-intercept form: If slopes are same but y-intercepts are different, then linear system has _____________________

If slopes are same and y-intercepts are same, then linear system has _______________________ If slopes are different and y-intercepts are different, then linear system has __________________ You try: Determine the number of solutions of each linear system. 1) 3 yx

22 yx

2) 1064 yx 532 yx

3) 142 yx 263 yx

Ch. 7. 6 HW: p. 448 #4, 5, 7



Chapter7‐Review 1. Solve by graphing.

a) 83 xy

23

1 xy

Solution: ______x ______y Or ____)(____,

b) 62 yx 1532 yx

Solution: ______x ______y Or ____)(____,

2. Solve by substitution.

xy 3 524 yx

3. Solve by elimination.

523 yx 032 yx

4. Solve.

132

yx

13

2

4

yx

HW: p.452 #10, 15, p.455 #2, 5

Documents

Ch. 7 - Systems of Linear Equations - Block A fileStandard form: Ax By C Linear equations do NOT have to be written in one of the above forms. All linear equations, regardless of which