Understanding Mathematical Terms

Refer to the English-Spanish Glossary, which starts on textbook page A39, if you need help with a definition or finding a textbook page with an example for a vocabulary word.

Explorations

Read and work through the Explorations 1, 2 and 3 and Communicate Your Answer on page 231. Then, check your answers below.

Answers to Explorations and Communicate Your Answer

Exploration 1 (page 231)

1. Equation 1: x + y = 4.5; Equation 2: x + 5y = 16.5
2. 4y = 12; Solve the resulting equation for y. Then substitute the value of y into one of the original equations and solve for x; (1.5, 3); Drinks cost $1.50 and sandwiches cost $3.

Exploration 2 (page 231)

1. (1, –3); yes; Sample answer: method 2
2. (2, 2); yes; Sample answer: method 2
3. (–1, 3); yes; Sample answer: method 1

Exploration 3 (page 231)

1. no; Sample answer: Multiply each side of Equation 2 by –2.
2. (2, 3)

Communicate Your Answer (page 231)

4. Multiply, if necessary, one or both equations by a constant so one pair of like terms has the same or opposite coefficients. Add or subtract the equations to eliminate one of the variables. Solve the resulting equation. Then substitute the value of the variable found into one of the original equations and solve for the other variable.
5. When one of the variables has the same or opposite coefficients in both equations; Sample answer: x + 3y = 2 and –x + 5y = 7; when neither of the variables has the same nor opposite coefficients in both equations; Sample answer: 3x – 2y = 12 and 2x – 3y = –15
6. Multiplication Property of Equality; Multiplying each side of an equation by the same nonzero number produces an equivalent equation.

Section 5-3 Lesson (pages 232-234)

Study and work through Examples 1 through 3. Remember, what you do to one side you must do the other side and when you change the direction of the sign. Practice with the Monitoring Progress problems as you go, and then check your answers below.

Answers to Monitoring Progress (pages 233-234)

1. (1, 2)
2. (6, –6)
3. (2, 5)
4. Sample answer: –x + 2y = 16 and –3x + y = –8; (6.4, 11.2)