Review Unit 6: Systems of Equations
Review Unit 6: Systems of Equations
Review Unit 6: Systems of Equations
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<strong>Review</strong> <strong>Unit</strong> 6: <strong>Systems</strong> <strong>of</strong> <strong>Equations</strong>No calculator necessary. Please do not use a calculator.<strong>Unit</strong> 6 Goals• Understand that solutions to a system <strong>of</strong> two linear equations in two variables correspond to points <strong>of</strong>intersection <strong>of</strong> their graphs, because points <strong>of</strong> intersection satisfy both equations simultaneously. (8.EE.8a)• Solve systems <strong>of</strong> two linear equations in two variables algebraically, and estimate solutions by graphing theequations. Solve simple cases by inspection. (8.EE.8b)• Solve real-world and mathematical problems leading to two linear equations in two variables (8.EE.8c)Estimate the solution to the system <strong>of</strong> equations using the graph provided. Give your answer in the form <strong>of</strong> apoint.1. 3 2 2. 2 5 2 4 Estimate the solution to the system <strong>of</strong> equations by graphing each equation on the graph provided. Give youranswer in the form <strong>of</strong> a point.3. 3 7 4. 2 7 3 3233
Estimate the solution to the system <strong>of</strong> equations by graphing each equation on the graph provided. Give youranswer in the form <strong>of</strong> a point.5. 2 2 4 6. 2 8 10Solve the following systems <strong>of</strong> equations using any method. There could be one solution, infinite solutions, orno solution.7. 3 3 9 8. 2 8 3 2 119. 5 10. 6 2 8 4 3 411. 1 12. 3 52 2 4 6 2 10234
Write and solve equations for the following situations. YOU MAY USE A CALCULATOR ON THESE!13. Kera sells glasses <strong>of</strong> Koolaid for $1 each and lemon shakeups for $3 each. One day she sold 10 more lemonshakeups than glasses <strong>of</strong> Koolaid, and she made a total <strong>of</strong> $190 selling. How many glasses <strong>of</strong> Koolaid and lemonshakeups did she sell?14. The perimeter <strong>of</strong> a rectangle is 14 cm. The length <strong>of</strong> the rectangle is 4 cm more than twice the width. Findthe dimensions <strong>of</strong> the rectangle.15. A 12% brine solution was mixed with a 16% brine solution to produce a 15% brine solution. How much <strong>of</strong>the 12% brine solution and how much <strong>of</strong> the 16% brine solution were used to produce 40 L <strong>of</strong> the 15% solution?16. One customer purchased 2 lattes and 1 hot chocolate for $9. The next customer purchased 2 lattes and 3 hotchocolates for $13. How much did each latte and each hot chocolate cost?235
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