# Types of Solution of Equations Graphed

Use this template to insert your answers for the assignment. Please use one of the four methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Remember that your work should be clear and legible.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.

1. Describe the three types of solutions systems of equations have when graphed.

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2. The sum of two numbers is 30 and their difference is 2. Find the two numbers by writing and solving a system of equations.

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3. Two apples and three pears cost $3.45. Three apples and five pears cost $5.55. Find the cost of each type of fruit.

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4. Mary has a total of $5000 invested in two accounts. One account pays 5% and the other 8%. Her interest in the first year was $331. Write and solve a system of equations to find out how much she has invested in both accounts.

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5. Terry is mailing two boxes. Together they weigh 21 lbs. If the smaller box is 5 lbs. less than the larger one, how much does each box weigh? Write and solve an equation that models this scenario.

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6. The length of a pool is 3 feet more than twice its width. If the perimeter of the pool is 72 feet, find the dimensions of the pool by writing and solving a system of equations.

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7. A desk and a chair cost $200 as a set. If the desk costs four times more than the chair, how much does each one cost. Write and solve using a system of equations.

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8. Rachel has 15 coins with a value of $2.85. If the coins are either dimes or quarters, how many of each coin does she have? Write and solve using a system of equations.

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9. A music concert was attended by 450 people. Adult tickets sold for $70 and children's tickets for $40. If total sales were $27,750, how much of each ticket was sold?

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10. A party planner can spend a maximum of $5000 on food. If the chicken dinner (x) costs $20 and the steak dinner (y) costs $25, make a graph of the region that shows the possibilities for the number of chicken and steak dinners that can be purchased while still staying within budget. Shade the solution set.

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11. What is an expression? What is an equation? What are the similarities and differences between both of them? Write 1-2 examples of each.

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12. What are the steps for solving an equation? Show an example. What and how are inverse operations used? Are equations and inequalities solved the same way? If not, how are they different? What is the rule to flip the inequality sign? Create 2 inequality problems containing a minimum of 3 steps for your peers to solve.

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13. What are the 3 methods to graph a line? Choose 1 of the methods and describe how to graph a line using an example equation? Why do you prefer this method?

Create 1 equation and ask your peers to describe the graph using 1 of the 3 methods.

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14. What are the three methods for solving systems of equations? Do they all produce the same answer? Which method do you prefer to use and why? Create 1 system of equations and ask your peers to solve it using 1 of the 3 methods.

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15. What are three laws of exponents (for multiplication, division, and powers)? Write and explain each law. Why do we use exponents in scientific notation (you can provide an example)? Write 2 problems containing exponents for your peers to simplify.

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#### Solution Summary

All questions have been answered in the file attached. The work is shown in the file.