1. What is the solution to the system of linear equations?

2x – 5y = 14

7x + 6y = -2

2. Heather is 6 years younger than 5 times her daughter's age. The sum of their ages is greater than 90.

What is the youngest age Heather's daughter can be?

3. What is the interval notation for the compound inequality?

-5 > a or a > 4

4. Plot the inequality on the number line

x < -2 or x > 5

5. Solve for x.

-14 < 3x - 2 x < 7

6. Solve for x.

-14 < 3x + 5 or 1/2x + 5 > 7

thank you for the help

Guest Aug 22, 2018

#1**+2 **

1.

2x – 5y = 14 multiply through by 6 → 12x - 30y = 84 (1)

7x + 6y = -2 multiply through by 5 → 35x + 30y = -10 (2)

Add (1) and (2)

47x = 74

x = 74 / 47

And using 2x - 5y = 14 we have

2(74/47) - 5y = 14

148 / 47 - 5y = 14

148/47 - 14 = 5y

148 /47 - 658 / 47 = 5y

-510 / 147 = 5y divide both sides by 5

-102 / 147 = y

CPhill Aug 22, 2018

#2**+2 **

2. Heather is 6 years younger than 5 times her daughter's age. The sum of their ages is greater than 90.

What is the youngest age Heather's daughter can be?

Let her daughter's age = D

Heather's age is 5D - 6

And we have that

D + 5D - 6 > 90 simplify

6D - 6 > 90 add 6 to both sides

6D > 96 divide both sides by 6

D > 16

Her daughter must be at least 17

CPhill Aug 22, 2018