Eli is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 3 people and large rooms that can hold 5 people. Eli reserved twice as many large rooms as small rooms, which altogether can accommodate 65 guests. Determine the number of small rooms reserved and the number of large rooms reserved.

5 small rooms and 10 large rooms.

Step-by-step explanation:

Let be "s" the number of  small rooms reserved and "l" the number of large rooms reserved.

Using the information given in the exercise, set up a System of equations:

Now, in order to solve the System of equations, you can use the Substitution method. The steps are:

1. You must substitute the second equation into the first equation:

2. Now, you must solve for the variable "s" in order to find its value:

3. Finally, substitute the value of "s" into the second equation and evaluate, in order to find the value of "l". You get that this is:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3