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Solving Equations pt. 2

Solving Equations pt. 2. Literal Equations and Formulas. What is a Literal Equations. A literal equation is an equation that involves two or more variable.

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Solving Equations pt. 2

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  1. Solving Equations pt. 2 Literal Equations and Formulas

  2. What is a Literal Equations A literal equation is an equation that involves two or more variable. The solution of a literal equation can be found using the properties of equality and inverse operations to form a series of simpler equations. The properties of equality can be used repeatedly to isolate any particular variable. You can treat the variables that you are not solving for as constants.

  3. A Literal Equation MENU Pizza $10 Sandwiches $5 What is the relationship between the number of pizzas and the number of sandwiches you can buy? [As the number of pizzas increases, the number of sandwiches decreases.] You are ordering pizzas and sandwiches. You have a budget of $80. How many sandwiches can you buy if you buy 4 pizzas? 5 pizzas? Explain your answer. Process Build a chart. Use the number of pizzas required to calculate the money remaining for sandwiches. Use an equation.

  4. Rewriting a Literal Equation • In this lesson, you will learn to solve problems using equations in more than one variable. • When you work with literal equations, you can use the same methods you used in solving one, two, and multi-step equations. The equation 10x + 5y = 80, where x is the number of pizzas and y is the number of sandwiches, models the pizza problem on the previous slide. How many sandwiches can you buy if you buy 3 pizzas? 6 pizzas? Continue on next slide

  5. Rewriting a Literal Equation If you buy 3 pizzas, you can buy 10 sandwiches. If you buy 6 pizzas, you can buy 4 sandwiches.

  6. Rewriting a Literal Equation with Only Variables Remember: When a literal equation contains only variables, treat the variables you are not solving for as constants. When you rewrite literal equations, you may have to divide by a variable or variable expression. When you do so in this lesson, assume that the variable or variable expression is not equal to zero because division by zero is not defined (cannot be done). What equation do you get when you solve ax – bx = c, solve for x?

  7. FORMULAS TRY TO MEMORIZE

  8. What is a Formula? A formula is an equation that states a relationship among quantities. Formulas are special types of literal equations. Some common formulas are given below. Notice that some of the formulas use the same variables, but the definitions of the variables are different.

  9. What is a Formula? Memorize these

  10. Rewrite a Geometric Formula What is the radius of a circle with a circumference 64 ft? Round to the nearest tenth. Use 3.14 for π Because you need to find the radius, isolate the variable r. Because you are given the Circumference use the circumference formula.

  11. Rewriting a Formula The monarch butterfly is the only butterfly that migrates annually north and south. The distance that a particular group of monarch butterflies travels is shown. It takes a typical butterfly about 120 days (time) to travel one way. What is the average rate at which a butterfly travels in miles per day? Round to the nearest mile per day. The butterflies travels 1700 miles(distance) from Indiana to Mexico. You are looking for the rate so isolate the variable r.

  12. Do you know HOW? Solve each equation for the given variable. -2x + 5y = 12 for y a – 2b = -10 for b mx + 2nx = p for x C = for F Jonah is planting a rectangular garden. The perimeter of the garden is 120 yd, and the width is 20 yd. What is the length of the garden?

  13. Do you UNDERSTAND? Classify each equation below as a formula, a literal equation, or both. c = 2d y = 2x – 1 A = P = 2l + 2w How is the process of writing literal equations similar to the process of solving equations in one variable? How is it different?

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