|
Title: You now have had practice solving equations with one variable and equations with two variables? Post by: irina on Oct 6, 2012 You now have had practive solving equations with one variable and equations with two variables. Compare equations with one variable to equations with variables. How are they alike? How are they different?
Title: You now have had practice solving equations with one variable and equations with two variables? Post by: sms305 on Oct 6, 2012 Hello!
An one variable equation is a line in a two-dimensional "space". For example 2x-5=3 => x=4 represents a line parallel to x-axis that start from the number 4. In fact it represent a constant number. Now, if u have a two variable equation like a)y-2x=5 => y=2x+5 it represents the linear equation in two-dimensional space. b) x^2+y^2=9 is a two variable equation too, but now represents a cirle. c) x^2-y=0=> y=x^2 represents the quadratic equation in two-dimensional space. d)y^3-x=5 represents a cubic equation etc.... But if u have a 3 variable equation, like x+y=z=2 or x^2-2y+z=1, it represents a curve in a 3-dimensional space. To conclude: A)1-variable= representation of a number (2D) B)2-variables= curves in two dimensions (2D) C)3-variables= curves in three dimensions (3D) In Physics many times, are used 4 variable equations. So u have x,y,z as space variables and t as the time variable. A 4-dimensional equation cannot be drawn, it's a dynamical system that always changing (moving) Unlikely we are beings that living in a 4D Time-space and we cannot deeply understand(imagine) what a higher variable equation represents. |