What does the solution to a linear system represent??
444364
They are the values that make the equation true.  If the equation is true then the equation represents a straight line.
152511
Which function, Subsitution, Linear COmbination, Graph?
133024
y = 0.\n\nETA: That's if we're to assume that the value of x is constant between the equations.
196036
If you divide 2 to the second equation, you will notice that it is identical to the first one, so they are dependent to each other, and there are infinitely many solutions to this problem.\n\n^_^
236017
sorry i don't know mathematica but you can solve it easily using matlab. Enter rthe coefficient matrix as follows for example,\nA=[1 2 3 4; 2 3 3 4;........]\nand the right hand side\nb=[ 2 3 4 4]\nonly for illustration. ";"indicates columns.\nA/b solves this system and gives the solution vector x.
789048
It is linear because the current and voltage relationship can be described as a linear differential equation:\n\nI = dQ/dt = C * dV/dt
1093689
Not sure what you're driving at here...\n\nA system of linear equations is simply a number of linear equations that all have a common solution (intersecting point when graphed).\n\nA linear equation could be, by itself, considered a system of linear equations, but is more typically one of a few linear equations in a system.
895128
If by 'convert' to a linear function you mean approximate by a linear function, then a possible solution is given by the Taylor's expansion of the exponential function.\n\nConsider a point x0, then the linear approximation of y around x0 is given by:\n\ny(x) = e^(x0+a) + e^(x0+a) * (x+a-x0) ,\n\nwhich is linear in x.  Obviously this is only an approximation as the Taylor expansion of the exponential function will involve a very large number of higher order (i.e. quadratic, cubic etc) terms in the right hand side of the equation.
417878
linear.  Linear means "to the first power", nonlinear means "to the second power (squared)", "to the third power" or higher (or some other function).  \n\nPerimeter of a square = 4 x length of side.\nwhich means \n4 x "length of side to the first power"\n\ndouble the length of the side and you double the perimeter; triple it and you triple the perimeter.
962302
You tell an equation is linear if there's a simple relationship between "x" and "y".\n\nIf you can say that "y is 2 lots of x, plus some constant number" or "y is half of x plus some constant number", that's a linear relationship.\n\nNote that the constant number can be 0!\n\nWritten formally, that means y = ax + b, where "a" is the simple relationship and "b" is some constant number.\n\nIf you need to transform "x" in any other way, it's non-linear.
730660
This equation has a solution when x = 0 or y = 0\n\n- - - - - - - - - - - -\n\nx = 0\n\n5x - 28 = 12 + 3y\n\n5(0) - 28 = 12 + 3y\n\n0 - 28 = 12 + 3y\n\n- 28 = 12 + 3y\n\n- 28 - 12 + 12 + 3y - 12\n\n- 30 = 3y\n\n- 30/3 = 3y/3\n\n- 10 = y\n\nThe answer is y = - 10\n\n- - - - - - - - - - - - - - - -\n\ny = 0\n\n5x - 28 = 12 + 3y\n\n5x - 28 = 12 + 3(0)\n\n5x - 28 = 12 + 0\n\n5x - 28 + 28 = 12 + 28\n\n5x = 30\n\n5x/5 = 30/5\n\nx = 6\n\nThe answer is x = 6\n\n- - - - - - - - - \n\nx = 6\n\ny = - 10\n\n- - - - - - - - - -\n\nThe solution set is { 6, - 10 }\n\n- - - - - - - - - - - - -s-
737727
What does C represent?  If C is a constant, then this doesn't converge.\nWhat is the context?  What is the name of the class, chapter and section that this comes from?
22881
Its a linear equation with d as the variable.
471523
A linear equation in two variables describes a relationship in which the value of one of the variables depends on the value of the other variable. In a linear equation in x and y, x is called x is the independent variable and y depends on it. We call y the dependent variable. If the variables have other names, yet do have a dependent relationship, the independent variable is plotted along the horizontal axis. Most linear equations are functions (that is, for every value of x, there is only one corresponding value of y). When you assign a value to the independent variable, x, you can compute the value of the dependent variable, y. You can then plot the points named by each (x,y) pair on a coordinate grid. The real importance of emphasizing graphing linear equations with your students, is that they should already know that any two points determine a line, so finding many pairs of values that satisfy a linear equation is easy: Find two pairs of values and draw a line through the points they describe. All other points on the line will provide values for x and y that satisfy the equation.\n\n\nA linear equation is special because: \n-It has one or two variables. \n-No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. \n-When you find pairs of values that make the linear equation true and plot those pairs on a coordinate grid, all of the points for any one equation lie on the same line. Linear equations graph as straight lines.
665576
x^2<4x\n\ncase 1: x<=0\nno solution\n\ncase 2: x>0\ndivide by x\nx<4\n\ntherfore the solutions are 0<x<4
818907
Linear means that the relationship between two variables varies in the same way, except by a constant factor (A) and a constant offset (B).  y = A*x + B\n\nThe volume of water in a tank, and its mass are linearly related.  [m = p*V, where m is the mass, p (rho) is the density of water, which is constant (converted to the units of m and V), and V is the volume of water.  The units of m and V are usually kg and liters, or lbs and ft^3.]\n\nAny other kind of relationship is non-linear, which includes most every process in the real world.  Non-linear relationships usually seem to result from friction/entropy/inefficiency or from forces like magnetic fields, electric fields, or gravity, or well pretty much everything real.
268125
just investigate for example ODE y"=-y and then add to the left part increasingly small non-linearity +c*y^2 and find solution of the first order of c - you will see how different modes interact with each other.