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

−8x − 7y = 96

−3x + 5y = −25

 

2. Marty is 3 years younger than 6 times his friend Warren's age. The sum of their ages is greater than 11.

What is the youngest age Warren can be?

 

Enter your answer, as a whole number, in the box.

 

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

x ≤ 3  or  x > 7

 

A.(−∞, 3) or [7, ∞)

B. (3,7]

C. [3,7)

D. (−∞, 3] or  (7, ∞)

AngelRay  Dec 16, 2017

Best Answer 

 #1
avatar+7048 
+1

1.

 

-8x - 7y  =  96      multiply this equation through by  5  to get      -40x - 35y  =  480

-3x + 5y  =  -25    multiply this equation through by  7  to get      -21x + 35y  =  -175

 

(-40x - 35y) + (-21x + 35y)   =   480 + -175

 

-61x  =  305

x  =  -5              Use this value for  x  in the second given equation to find  y  .

 

-3(-5) + 5y  =  -25

15 + 5y  =  -25

5y  =  -40

y  =  -8

 

 

2.    Let Marty's age be  " m " ,  and let Warren's age be  " w " . The problem tells us that...

 

m  =  6w - 3

                              and

m + w  >  11

 

Plug in   6w - 3   for   m   into the inequality.

 

6w - 3  + w  >  11      Add  3  to both sides and combine like terms.

7w  >  14

w  >  2        Warren has to be older than  2  .

 

So if his age has to be a whole number, the youngest he can be is  3 .

 

 

3.    (−∞, 3]  or  (7, ∞)

hectictar  Dec 16, 2017
Sort: 

1+0 Answers

 #1
avatar+7048 
+1
Best Answer

1.

 

-8x - 7y  =  96      multiply this equation through by  5  to get      -40x - 35y  =  480

-3x + 5y  =  -25    multiply this equation through by  7  to get      -21x + 35y  =  -175

 

(-40x - 35y) + (-21x + 35y)   =   480 + -175

 

-61x  =  305

x  =  -5              Use this value for  x  in the second given equation to find  y  .

 

-3(-5) + 5y  =  -25

15 + 5y  =  -25

5y  =  -40

y  =  -8

 

 

2.    Let Marty's age be  " m " ,  and let Warren's age be  " w " . The problem tells us that...

 

m  =  6w - 3

                              and

m + w  >  11

 

Plug in   6w - 3   for   m   into the inequality.

 

6w - 3  + w  >  11      Add  3  to both sides and combine like terms.

7w  >  14

w  >  2        Warren has to be older than  2  .

 

So if his age has to be a whole number, the youngest he can be is  3 .

 

 

3.    (−∞, 3]  or  (7, ∞)

hectictar  Dec 16, 2017

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