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Lesson Plan 1: Left Hand, Right Hand - Solving Systems of Equations
The questions below dealing with systems of linear equations have been selected from various state and national assessments. Although the lesson above may not fully equip students with the ability to answer all such test questions successfully, students who participate in active lessons like this one will eventually develop the conceptual understanding needed to succeed on these and other state assessment questions.
Taken from California High School Exit Examination (Spring, 2002):
7x + 3y = -8
-4x - y = 6
What is the solution to the system of equations shown above?
A. (-2, -2)
B. (-2, 2) (correct answer)
C. (2, -2)
D. (2, 2)
Taken from the Texas Assessment of Knowledge and Skills (Spring 2003):
The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 85 centimeters?
- l = w + 3
2(l + w) = 85
- l = 3w
2l + 6w = 85
- l = 3w
2(l + w) = 85 (correct answer)
- l = w + 3
2l + 6w = 85
Taken from the Texas Assessment of Knowledge and Skills (Spring 2003):
Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. Then he solved the system by graphing. How many coins of each type did Marcos have?
A. (6, 9) (correct answer)
B. (5, 10)
C. (9, 6)
D. (10, 5)
Taken from the Connecticut Academic Performance Test (Spring, 2002):
Industrial Electrical Use. A utility company offers electricity to industrial users at a rate of 8 cents per kilowatt-hour. The company also offers a fixed annual rate of $1,200,000 for unlimited use of electricity. Graph each of these two rates as a line on the grid in your answer booklet. Explain why a large industrial user of electricity would choose to pay the fixed annual rate. Use the information in your graph to support your answer.
Solution: If a user needs less than 15,000,000 kilowatt-hours of electricity in a year then the 8 cents per kilowatt-hour rate would be cheaper than the fixed rate. But, if they required more than 15,000,000 kilowatt-hours, then the fixed rate would cost less money. If the user requires exactly 15,000,000 kilowatt-hours,
then the cost of the two plans would be the same.
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