Oscillation
Oscillation refers to the repetitive variation or movement around an equilibrium point or a mean value of a system. It is a type of periodic motion where a physical object or a system undergoes a repeated cycle of movement around a fixed point or axis. Examples of oscillation include the back-and-forth motion of a pendulum, the vibration of a guitar string, or the alternating current in an electrical circuit. Oscillation is a fundamental concept in physics, engineering, and many other fields of science, as it plays a critical role in understanding and describing various phenomena, including waves, sound, and light.
Hi Bot!
Solve the system of equations.
6x–5y=27
3x+5y=36
Adding the two equations, we get:
6x - 5y + 3x + 5y = 27 + 36
Simplifying it, we get:
9x = 63
Dividing both sides by 9, we get:
x = 7
Now substituting this value of x in any of the equations we can find the value of y.
Using the first equation:
6x - 5y = 27
6(7) - 5y = 27
42 - 5y = 27
-5y = -15
y = 3
Therefore, the solution for the given system of equations is x=7 and y=3.
Solve the system of equations.
2x+8y=8
2x−4y=−16
To solve the system of equations, we can use the elimination method by adding the two equations which will eliminate x and give us the value of y.
(2x+8y) + (2x-4y) = 8 + (-16)
Simplifying the equation, we get:
4x = -8
Dividing both sides by 4, we have:
x = -2
Now substituting this value of x in any of the equations, we can find the value of y. Let's use the first equation:
2x + 8y = 8
2(-2) + 8y = 8
-4 + 8y = 8
8y = 12
y = 3/2
Therefore, the solution for the given system of equations is x = -2 and y = 3/2.
incorrect
can you try again
I apologize for the mistake in my previous response. Let me solve the system of equations correctly.
The given system of equations is:
2x + 8y = 8 ...(1)
2x - 4y = -16 ...(2)
We can use the elimination method by adding the two equations which will eliminate x and give us the value of y.
(2x + 8y) + (2x - 4y) = 8 - 16
Simplifying the equation, we get:
4x = -8
Dividing both sides by 4, we have:
x = -2
Now substituting this value of x in any of the equations, we can find the value of y. Let's use the first equation:
2x + 8y = 8
2(-2) + 8y = 8
-4 + 8y = 8
8y = 12
y = 3/2
Therefore, the solution for the given system of equations is x = -2 and y = 3/2.
Bot, how many solutions does the system of equations have?
8x−6y=48
8x+6y=48
Let's solve the system of linear equations:
8x - 6y = 48 ...(1)
8x + 6y = 48 ...(2)
To eliminate y, we can add the two equations:
(8x - 6y) + (8x + 6y) = 48 + 48
16x = 96
x = 6
Substituting the value of x in any of the equations, we can find y:
8x - 6y = 48
8(6) - 6y = 48
48 - 6y = 48
-6y = 0
y = 0
Therefore, the solution to the system of equations is x = 6 and y = 0.
Since we were able to find a unique solution for both variables x and y, the system of equations has only one solution, also known as a unique solution.
How many solutions does the system have?
12x−15y=18
4x−5y=6