Which of the following is a solution to the system of equations? y= 3x-2 6 + y=-x

x=-1  y = -5

Step-by-step explanation:

y= 3x-2  

6 + y=-x

Substitute the first equation into the second equation

6 +y =-x

6+ (3x-2) = -x

Combine like terms

4 + 3x = -x

Subtract 3x from each side

4 +3x -3x = -x -3x

4 = -4x

Divide by -4

4/-4  = -4x/-4

-1 =x

Now we need to find y

y= 3x-2

y = 3(-1) -2

  = -3-2

   = -5

(-1, -5)

Step-by-step explanation:

We can solve this system using substitution.  y = 3x - 2, so replace "y" in the second equation with "3x - 2:"

6 + (3x - 2) = -x, or 6 + 3x - 2 = -x

Group like terms together:  3x + x = -6 + 2.

Then 4x = -4, and x = -1.

Subst. -1 for x in the first equation:  y = 3(-1) - 2, or y = -5.

Then the solution is (-1, -5).

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages