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MATH 10C ASSIGNMENT D7 - M7A3 33 Marks Show your work.

Try This 2 1. Use the following information to answer the following question.

Statement 1: All triangles have three sides.

Statement 2: A bandana is in the shape of a triangle.

What can you conclude about bandanas from the two statements? (1) Answer: This particular bandana has three sides 2. Consider the two mathematical statements.

Statement 1: 10 = 3 + 7 Statement 2: Write a third statement that combines the information from statements 1 and 2. (1) Answer: 3+7=2x5

Try This 3 3. Consider the following linear system: Equation 1: x  2y  8 Equation 2: 3x  y  10 a. Isolate one of the variables in the Equation 1. (1) Answer: x = 2y + 8 b. Substitute the Equation 2 into Equation 1. (1) Answer: 3(2y + 8) + y = 10 c. Expand the resulting expression, and solve for the unknown variable. (1) Answer: 6y + 24 + y = 10 7y = -14 y = -2 d. Substitute the answer from 3c. into one of the original equations to obtain the value of the other unknown. (1) This study source was downloaded by 100000859607764 from CourseHero.com on 01-07-2023 14:32:25 GMT -06:00

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Answer: x = -4 +8 x=4 e. Verify your solution by substituting the obtained values into the original system. (1) Answer: (4) - 2(-2) = 8 3(4) + (-2) = 10

Try This 4 4. Solve the following systems of linear equations by first substituting for y. (6) Systems of Linear Equations a. b. c.

y  3x  2 x  y  14 y  3x

y  x  24 y  x7 x  y  17

Answer x=3 y = 11 x = -12 y = 36 x = 12 y=5

5. Solve the following systems of linear equations. Check your answers. (6) Systems of Linear Equations a.

b.

1 y  x 5 3 y x   13 5 yx 5 2 3 x y4 4

Answer x = 97/8 y=

1 2x  3 3 3y x  12 2

3y 

c.

6. Jaret and Helen are going to solve the following system of equations.

2x  3y  6

3x  y  20  0

As an initial step, Jaret decides to isolate x in the first equation.

As an initial step, Helen decides to isolate y in the second equation. a. Solve this system using Jaret’s method. (2) Answer: This study source was downloaded by 100000859607764 from CourseHero.com on 01-07-2023 14:32:25 GMT -06:00

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b. Solve this system using Helen’s method. (2) Answer:

c. Explain which method you prefer. (1) Answer:

7. The graph represents the solution to the following linear system. y  2x  3 6x  3y  13

a. State the coordinates of the point of intersection by reading the graph. (1) Answer:

b. Solve the linear system using the substitution method. (2) Answer:

c. Compare your answers for parts a and b. What is the advantage of the algebraic approach? (2) Answer:

Try This 5 8. The admission fee for the chuckwagon races at the Grande Prairie Stampede is $10.00 for children and $16.00 for adults. On a certain day, 2200 people enter the fair and $30 544 is collected. Determine the number of children and the number of adults that attended on this day. (4) This study source was downloaded by 100000859607764 from CourseHero.com on 01-07-2023 14:32:25 GMT -06:00

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Answer: Equation 1: Equation 2: Number of children: Number of adults: Once you have completed these questions, submit your completed assignment to the D7 dropbox for marking.

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