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**Chapter 10: Solving Linear Equations**

Regular Math

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**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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**Try this one on your own…**

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?

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**Solving Two-Step Equations…**

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Try these on your own…

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**Section 10.2: Solving Multistep Equations**

Solving Equations That Contain Like Terms

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**Solving Equations That Contain Fractions**

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**Finding and Using the Least Common Denominator**

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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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Try these on your own…

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**Section 10.3: Solving Equations with Variables on Both Sides**

Clear Fractions Combine Like Terms Get the Variable on Only One Side of the Equation Undo Addition or Subtraction Undo Multiplication or Division

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Try these on your own…

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**Solving Multistep Equations with Variables on Both Sides**

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Try these on your own…

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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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**Try this one on your own…**

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?

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**Section 10.4: Solving Multistep Inequalities**

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Try these on your own…

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Try these on your own…

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**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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**Try this one on your own…**

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?

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**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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Try these on your own… a – b + 1 = c for a a – b + 1 = c for b

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**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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**Try these on your own… V = IR for R**

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

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**Solve for y and graphing…**

2x + 3y = 6

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**Try this one on your own…**

3x + 2y = 8

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**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.

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**Identifying Solutions of a System of Equations**

2x + 3y = 8 x – 4y = 15 (-2 , 4) (7 , -2) (11 , -1)

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**Solving Systems of Equations**

y = x + 3 y = 2x + 5 y = x – 4 y = 2x - 9

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x + y = 5 x – 2y = -4 3x + y = 8 4x – 2y = 14

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California Standards AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions.

California Standards AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions.

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