Chapter 10: Solving Linear Equations

Regular Math

Section 10.1: Solving Two-Step Equations

Chris’s landscaping bill is $380. The plants cost $212, and the labor cost $48 per hour. How many hours did the landscaper work?

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The mechanic ‘s bill to repair Mr. Wong’s car was $650. The mechanic charges $45 an hour for labor, and the parts that were used cost $443. How many hours did the mechanic work on the car?

Solving Two-Step Equations…

1354

p

7.15.28.1 m

69

4

k

Try these on your own…

93

4

6.63.17.2

2273

y

m

n

Section 10.2: Solving Multistep Equations

Solving Equations That Contain Like Terms

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Solving Equations That Contain Fractions

7

1

7

5

7

3

y

Finding and Using the Least Common Denominator

2

7

6

1

43

2

pp

Money Application…

Carly has a $10 gift certificate for her favorite restaurant. After a 20% tip was added to the bill, the $10 was deducted. The amount she paid was $4.40.What was her original bill?

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3

2

9

17

29

7

4

3

4

7

4

5

372368

xx

n

xx

Section 10.3: Solving Equations with Variables on Both Sides

1. Clear Fractions

2. Combine Like Terms

3. Get the Variable on Only One Side of the Equation

4. Undo Addition or Subtraction

5. Undo Multiplication or Division

aa 332

vv 7574

25 gg

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xx 64

www 47539

Solving Multistep Equations with Variables on Both Sides

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6

7

3

1

4

3

2 w

ww

Try these on your own…

10

7

4

3

5

3

5

152841510

yyy

zzz

Sports Application…

Elaine runs the same distance every day. On Mondays, Fridays, and Saturdays, she runs 3 laps on the track, and then runs 5 more miles. On Tuesdays and Thursdays, she runs 4 laps on the track, and then runs 2.5 more miles. On Wednesdays, she just runs laps. How many laps does she run on Wednesday?

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Jamie spends the same amount of money each morning. On Sunday, he bought a newspaper for $1.25 and also two doughnuts. On Monday, he bought a newspaper for fifty cents and bought five doughnuts. On Tuesday, he spent the same amount of money and bought just doughnuts. How many doughnuts did he buy?

Section 10.4: Solving Multistep Inequalities

342

2310

532

x

x

x

Try these on your own…

2579

837

1314

x

x

x

6

5

2

1

3

2

5423

x

xx

Try these on your own…

10

9

4

3

5

2

1542110

x

xx

Business Application…

The student council sells t-shirts with the school logo on them. The unit cost is $10.50 for the shirt and the ink. They have a fixed cost of $60 for silk screen equipment. If they sell the shirts for $12 each, how many must they sell to make a profit?

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A school’s Spanish club is selling bumper stickers. They bought 100 for $55, and have to give the company 15 cents for every sticker sold. If they plan to sell each bumper sticker for $1.25, how many do they have to sell to make a profit?

Section 10.5: Solving for a Variable

Solve for the indicated variable.

V – E + F = 2 for V

V – E + F = 2 for E

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a – b + 1 = c for a

a – b + 1 = c for b

Solve for the indicated variable. Assume all values are positive.

Solve the formula for area of a triangle for h. A = ½ bh

Solve the formula for surface area of a cylinder for h. S = 2(pi)(r squared) + 2(pi)radius(height)

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V = IR for R

Solve the formula for the area of a trapezoid for h. A = ½ h (base one + base two)

Solve for y and graphing…

2x + 3y = 6

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3x + 2y = 8

Section 10.6: System of Equations

A system of equations is a set of two or more equations that contain two or more variables.

A solution of a system of equations is a set of values that are solutions of all of the equations.

Identifying Solutions of a System of Equations

2x + 3y = 8 x – 4y = 15

a. (-2 , 4)

b. (7 , -2)

c. (11 , -1)

Solving Systems of Equations

y = x + 3 y = 2x + 5

y = x – 4 y = 2x - 9

x + y = 5 x – 2y = -4

3x + y = 8 4x – 2y = 14