You'd like to see how many baseball and soccer games you can attend this spring. Travel time for baseball games is 2 hours and soccer games is 1 hour. You would like to spend
no more than 15 hours traveling to the games. In total, you would like to attend at least
8 games.

x = 7

y = 1

Step-by-step explanation:

Let's assign the baseball to x and soccer to y. If each baseball game takes 2 hours and each soccer game takes 1 hour and we don't want to spend more than 15 hours we get the equation:

2x + y = 15

We have one equation now and we can get the second one from the number of games. We know that we want to attend 8 games therefore the number of baseball games plus the number of soccer games must be equal so we can use the equation:

x + y = 8

Now that we have our two equations we can use elimination to get x and y.

2x + y = 15

x + y = 8

isolate one of the variables from either equation. I chose to isolate x from the second equation givnig me:

x = 8 - y

now we can plug x back into the first equation to solve for y.

2x + y = 15

2(8 - y) + y = 15

16 - 2y + y = 15

-y = -1

y = 1

now that we have y we can solve for x by pluging it back into one of the origoriginal equations.

x = 8 - y

x = 8 - 1

x = 7

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

f(x)=2/3x-8, which give g(x) the greatest value.

step-by-step explanation: