Not sure what the equations are. please write them as y=3x+c or something like that They all run together. Then i can help you! Dr. Chuck aka math doc
That doesn't apply to "an" equation, but to a set of equations (2 or more). Two equations are:* Inconsistent, if they have no common solution (a set of values, for the variables, that satisfies ALL the equations in the set). * Consistent, if they do. * Dependent, if one equation can be derived from the others. In this case, this equation doesn't provide any extra information. As a simple example, one equation is the same as another equation, multiplying both sides by a constant. * Independent, if this is not the case.
Nothing yet. It only means that the equations you have are not independent ...one of them is a simple multiple of another one. All you can say so far is thatyou need another equation.
It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.
Here is a simple way to see it that will help you both understand and remember. Take two equations in two unknowns. You can generalize later. Make a 2x2 matrix using the coefficients only. Now if you multiply this equation by the vector (x,Y) written as a column and placed on the right side of the matrix and you have the 2 equations you started with. Now put the constants, that is to say what each equation is equal to, on the right side of the = sign. If you invert the coefficient matrix on the left, the 2x2 one, and multiply both sides by that inverse, the equation is solved. There is another method known as Cramer's rule that can help you to solve equations using matrices. I suggest you look that one up if you are interested or ask for some more help!
Is an equation of a straight line in 3 dimensions. It cannot be simplified further, and a solution for any of the variables requires another two [independent] equations.
This equation is not possible unless you are given another equation related to x and y. Then you could use simultaneous equations to solve this. However in this came this question is impossible
In a two step equation, you need to do another step.
If the two equations are linear transformations of one another they have the same solution.
That doesn't apply to "an" equation, but to a set of equations (2 or more). Two equations are:* Inconsistent, if they have no common solution (a set of values, for the variables, that satisfies ALL the equations in the set). * Consistent, if they do. * Dependent, if one equation can be derived from the others. In this case, this equation doesn't provide any extra information. As a simple example, one equation is the same as another equation, multiplying both sides by a constant. * Independent, if this is not the case.
If you have two equations give AND one parametric equation why do you need to find yet another equation?
Yes, for solving simultaneous equations.
Select one equation from a system of linear equations. Select a second equation. Cross-multiply the equations by the coefficient of one of the variables and subtract one equation from the other. The resulting equation will have one fewer variable. Select another "second" equation and repeat the process for the same variable until you have gone through all the remaining equations. At the end of the process you will have one fewer equation in one fewer variable. That variable will have been eliminated from the system of equations. Repeat the whole process again with another variable, and then another until you are left with one equation in one variable. That, then, is the value of that variable. Substitute this value in one of the equations from the previous stage to find the value of a last variable to be eliminated. Work backwards to the first variable. Done! Unless: when you are down to one equation it is in more than one variable. In this case your system of equations does not have a unique solution. If there are n variables in your last equation then n-1 are free to take any value. These do not have to be from those in the last equation. or when you are down to one variable you have more than one equation. If the equations are equivalent (eg 2x = 5 and -4x = -10), you are OK. Otherwise your system of equations has no solution.
There are several methods to do this; the basic idea is to reduce, for example, a system of three equations with three variables, to two equations with two variables. Then repeat, until you have only one equation with one variable. Assuming only two variables, for simplicity: One method is to solve one of the equations for one of the variables, then replace in the other equation. Another is to multiply one of the equations by some constant, the other equation by another constant, then adding the resulting equations together. The constants are chosen so that one of the variables disappear. Specifically for linear equations, there are various advanced methods based on matrixes and determinants.
Another straight line equation is needed such that both simultaneous equations will intersect at one point.
The general idea is to solve one of the equations for one variable - in terms of the other variable or variables. Then you can substitute the entire expression into another equation or other equations; as a result, if it works you should end up having one less equation, with one less variable.
A percent proportion is related to an equation because they are both used to indicate part of another whole. Equations are complex forms of fractions, sequence and they express logic.
If there are less distinct equations than there are variables then there will be an infinite number of solutions.For example, you may have 3 equations with 3 unknowns, but if one of those equations is a multiple of another there there are only 2 distinct equations:2x + 3y + 5z = 1x + y - 2z = 104x + 6y + 10z = 2Equation (3) here is twice equation (2) so there are effectively only 2 distinct equations for 3 unknowns and thus there will be an infinite number of solutions. If any two equations are parallel then there is no solution; if equation (3) above was 2x + 3y + 5z = 2, then there are no solutions - subtracting equation 1 from (the new) equation 3 would result in 0 = 1 which is nonsense.