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What are the three types of possible solutions to a system of equations?
Wiki User
∙ 10y ago
If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line.
If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.
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∙ 10y ago
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Is it possible to find three unknowns with two equations if the two equations are equal?
No i believe that with three unknowns you must have three equal equations. Hope this helps! -dancinggirl25
When solving a system of equations what does 4 equals 4 mean?
three things: 1) that the value of 4 is equal to the value of 4. 2) you did not obtain any revealing information. 3) your strategy for solving that system of equations was not good.
If a system of equation is inconsistent that means that the graphs of the two equations do not have any points in common what types of lines would be the result of an inconsistent system of equations?
In two dimensions, parallel ones. In three dimensions, either parallel or skew ones.
Is it possible to find three solutions of the equation x3 plus 2x2 plus 3x plus 6 equals 0 Explain why or why not?
The variable term, X^3, is a third order polynomial term and will render three solutions, though one of those may be zero.
Is it possible tofind three unknowns with two equations?
Answerno. A system with two equations and three variable is known as a parametric equation and can be simplified, generally, to one equation with two variables.You always need a number of equations equal to or greater than the number of variables you have to find any of the variables.If you have more varibles than equations you can eliminate a number of variables equal to the number of equations minus one.Edit: While this is correct, you can fudge an answer using a pseudoinverse. This minimizes one of the values, and then you can approximate the other two. Suppose you have:3x + 2y + 4z = 0x + 8y + 7z = 3You can call this A*b = y, whereA = [3,2,4;1,8,7]b = [x;y;z]y= [0;3]Then you can sayb=ay, wherea=A'(A*A')^(-1)' indicated the transpose, and ^-1 indicates the inverse.More explanation can be found at http://neurotheory.columbia.edu/~ken/math-notes/sabes.pdf
How many solutions does a system of linear equations in three variables have?
1
What are the three types of system of linear equations?
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
Kinds of system of linear equation in two variables?
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
How many solutions are there to the systems of equations?
I'm not 100% certain about what you're asking, but each function and relation can have different solutions, either one of the three ways. (Always dealing with two equations) This is based off my Grade 10 Knowledge One (Intersecting at one specific point) None (Parallel Lines) Coincident two lines with the same slope and intercept) Refer back to : " y=mx+b " equation if needed. If you are talking about the possible ways to find the solution (x,y), there are also three. Elimination, (Removing one variable to solve the equation) Substitution, (Knowing what x or y, and inputting in the second equation) Graphing, (By drawing both equations, This method is not very accurate)
What are the three different possible solutions of a linear system?
If the lines cross then there is one solution. If they are on top of each other then there are infinite solutions. If they are parallel then there are no solutions.
Is it possible to find three unknowns with two equations if the two equations are equal?
No i believe that with three unknowns you must have three equal equations. Hope this helps! -dancinggirl25
What is of system of equations?
It is essentially a list of equations that have common unknown variables in all of them. For example, a+b-c=3 4a+b+c=1 a-2b-7c=-2 would be a system of equations. If there are the same number of equations and variables you can usually, but not always, find the solutions. Since there are 3 equations and 3 variables (a, b, and c) in this example one can usually find the value of those three variables.
Three planes that intersect in a point?
The intersection of three planes is either a point, a line, or there is no intersection if any two of the planes are parallel to each other. This tells us about possible solutions to 3 equations in 3 unknowns. There may be one solution, no solution, or infinite number of solutions.
What are the three types of systems of linear equations and their characteristics?
Independence:The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
To solve a three variable system of equations you can use a combination of the elimination and substitution methods?
True. To solve a three variable system of equations you can use a combination of the elimination and substitution methods.
What are the three solutions for 4x-2y equals 8?
It is not appropriate to talk about "the" three solutions for this equations; the equation describes a straight line, and has an infinite number of solutions. Solve the equation for "y", substitute any value for "x", and calculate the corresponding value for "y", to get one opf these solutions.
Does the solution to a system of three equations in three variables is always one point?
No. There could be no solution - no values for x, y, and z so that the 3 equations are true.
