Question

9: If you were to solve the following system of equations by using a matrix, which of the following would be your coefficient matrix?
5x – y = 18
3x + 8y =15

A: [5 18]
[3 15]

B: [5 -1 18]
[3 8 15]

C: [5 -1]
[3 8]

D: [5 3]
[-1 8]

10: It is possible for a system of linear equations to have an infinite number of solutions
A: True
B: False

11: Let y = 3t + 6 be a linear function representing the distance from home for an ant t minutes after starting out from a location near its home. What does the number 3 represent in this function.?

A: The ant is 3 feet from its home after t minutes.
B: The ant started out 3 feet from its home.
C: The ant is crawling at 3 feet per minute.
D: The ant is moving 3 feet every 6 minutes.

Answer 1

Answer on Question #56376 – Math – Algebra

9. If you were to solve the following system of equations by using a matrix, which of the following would be your coefficient matrix?

$$\begin{array}{l} 5x - y = 18 \\ 3x + 8y = 15 \\ \end{array}$$

A: [5 18]

[3 15]

B: [5 -1 18]

[3 8 15]

C: [5 -1]

[3 8]

D: [5 3]

[-1 8]

Solution

C: [5 -1]

[3 8]

10. It is possible for a system of linear equations to have an infinite number of solutions

A: True

B: False

Solution

It is possible for a system of linear equations to have an infinite number of solutions. Example of a system that has infinite solutions:

$$\left\{ \begin{array}{l} y = 2x + 1, \\ 2x + 1 = 4x + 2; \end{array} \right. \quad \left\{ \begin{array}{l} y = 2x + 1, \\ 2y = 4x + 2 \end{array} \right.$$ $$2(2x + 1) = 4x + 2;$$ $$4x + 2 = 4x + 2;$$ $$4x - 4x = 2 - 2;$$ $$0 = 0, \text{ for any values of } x$$

Answer: A: True

11. Let $y = 3t + 6$ be a linear function representing the distance from home for an ant $t$ minutes after starting out from a location near its home. What does the number 3 represent in this function.?

A: The ant is 3 feet from its home after $t$ minutes.

B: The ant started out 3 feet from its home.

C: The ant is crawling at 3 feet per minute.

D: The ant is moving 3 feet every 6 minutes.

Answer: C: The ant is crawling at 3 feet per minute.

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