What is the solution set to the following system? {x+y=3 {x^2+y^2=9

There are two solutions

The first solution is (x,y) = (3,0)

The second solution is (x,y) = (0,3)

===============================================

Work Shown:

Isolate x in the first equation (subtract y from both sides)

x+y = 3

x = -y+3

Now plug this into the second equation. Isolate y.

x^2 + y^2 = 9

(-y+3)^2 + y^2 = 9 ... replace x with -y+3

y^2 - 6y + 9 + y^2 = 9 ... FOIL rule

2y^2 - 6y + 9 = 9

2y^2 - 6y = 0

2y(y-3) = 0

2y = 0 or y-3 = 0 .... zero product property

y = 0 or y = 3

--------------

If y = 0, then x is

x = -y+3

x = -0+3

x = 3

Therefore, x = 3 and y = 0 pair up to get the ordered pair (x,y) = (3,0) as one solution of this system

--------------

If y = 3, then x is

x = -y+3

x = -3+3

x = 0

Therefore, x = 0 and y = 3 pair up to get the ordered pair (x,y) = (0,3) as the other solution of this system

--------------

If you were to graph the two equations, you should find that the curves cross each other at (0,3) and (3,0). I've marked these two points as A and B respectively. The order of the solutions does not matter.

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

answer: since the question is talking about growth you have to use the growth formula which is inital amount (1 + growth)^time

step-by-step explanation:

the intial amount is 1200, the growth is 4.8, and the time is 7. plug those numbers into the equation, also i think you have to change 4.8 into a percent. but, i have forgotton how to do that. if this is a online class go on to the lesson.