Question

How many solutions will this system of equations have?

y = 3.5x − 3.5

y = −3.5x + 3.5 (2 points)




No solution


Infinite solutions


One solution


Two solutions

6.

(05.01)

Given the equation 3x − 4y = 8, which equation below would cause a consistent-dependent system? (2 points)




3x + 4y = −8


6x − 8y = 12


9x − 12y = 24


16x + 12y = −10

7.

(05.01)

A business has $11,080 to spend on new laptops and tablet computers for its salespeople. The laptops cost $515 each. The tablets cost $285 each. The business wants each salesperson to have either a laptop or a tablet. There are 30 salespeople. How many of each type of computer should the business buy? (2 points)




9 laptops and 21 tablets


11 laptops and 19 tablets


19 laptops and 11 tablets


21 laptops and 9 tab

Answer 1

Answer: One solution

Explanation:

y = 3.5x - 3.5

y = -3.5x + 3.5

Use substitution to solve:

3.5x - 3.5 = -3.5x + 3.5

+3.5x +3.5x

7.0x - 3.5 = 3.5

+3.5 +3.5

7.0x = 7.0

÷7.0 ÷7.0

x = 1.0

Since there is a solution for x, then there is one solution

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Answer: 9x - 12y = 24

Explanation:

consistent-dependent means they are the same line. This occurs when the given line is multiplied by a constant.

Let the constant be 3, then y = 3(3x - 4y = 8)

= 9x - 12y = 24

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Answer: 19 laptops and 11 tablets

Explanation:

Laptops (x): $515

Tablets (y): $285

EQ1: 515x + 285y = 11,080

EQ2: x + y = 30

Use elimination to solve:

515x + 285y = 11,080 ⇒ ⇒ ⇒ ⇒ 515x + 285y = 11,080

x + y = 30 ⇒ =515(x + y = 30) ⇒ -515x - 515y = -15,450

-230y = 4,370

÷-230 ÷-230

y = 19

x + y = 30

x + 19 = 30

x = 11