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

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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?

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, ∞)

Dec 16, 2017

#1
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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, ∞)

Dec 16, 2017

#1
+7354
+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