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Answered 2011-02-04 19:28:57

The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.

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There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.

False, think of each linear equation as the graph of the line. Then the unique solution (one solution) would be the intersection of the two lines.

A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?

Radial solutions are unique linear and non-linear formula equations used in math to explain the Laplacian equation. To calculate problems, scientist must determine the function based on the variable provided in the equation.

Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.

It is not possible to tell. The lines could intersect, in pairs, at several different points giving no solution. A much less likely outcome is that they all intersect at a single point: the unique solution to the system.

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.

This is the case when there is only one set of values for each of the variables that satisfies the system of linear equations. It requires the matrix of coefficients. A to be invertible. If the system of equations is y = Ax then the unique solution is x = A-1y.

No. The equation describes a straight line and the coordinates of any one of the infinitely many points on the line is a solution.

It is a linear equation in the two variables x and y. A single linear equation in two variables cannot be solved for a unique pair of values of x and y. The equation is that of a straight line and any point on the line satisfies the equation.

A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.

Cramer's rule is applied to obtain the solution when a system of n linear equations in n variables has a unique solution.

You know when an equation has a unique solution when there is only one variable in it. (APOLOGIES)(RESPONSE: the question was categorized under "Linear Algebra". x^2 is non-linear and is thus not allowed, nor are sin x, x^3, log x, 2^x, etc etc. However, you are correct if you consider non-linear equations. Unfortunately, I am not sure there is a method to determine the number of solutions to non-linear equation.)If there are more than one variable, each variable over the first will be free, and give you infinite solutions - with each additional variable adding another dimension to your solution.(RESPONSE: See above response with regards to this topic being categorized under "Linear Algebra". My statement is true in Linear Algebra. Furthermore, Row Reduced Echelon Form and augmented matrices are the most fundamental concepts in Linear Algebra. Under normal circumstances, I would agree with you. However, this question was categorized under "Linear Algebra", so I presumed that the person asking the question is a college student.)In general, you know that a system of equations has a unique solution when the row reduced echelon form of the augmented matrix has a pivot position in every column, except for the right most column which is the solution. If you do not have an augmented matrix, then the RREF will have a pivot position in every column.

Superposition theorem can be applied if- 1) The network is linear 2) The solution of the network is unique

So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.

Nobody can help you find a solution until you get another equation to go along with this one. Your equation has two variables in it ... 'x' and 'y' ... so it has no unique solution all by itself.

x = 3, y = 9 is one solution from infinite number of find another solution just choose any number for x, substitue it in the equation, for example if x = 1, y= 4 * 1 - 3 = 1, so 1 and 1 is another solution for y = 4 x - 3In this question there is only one equation which contains two variables, so there is no unique solution.we need other independent equation contains the variables x and y then we can solve these equations simultaneously, i.e. we can find finite number of solution (its one solution in linear equations)

Any 4 points in the Cartesian plane determine a unique equation that is of degree at most three (i.e., a "cubic" equation). It is, of course, possible that the 4 points actually lie on a degree two ("quadratic"), a degree one ("linear"), or a degree zero ("constant") equation. However, if the 4 points do not lie on a constant, linear, or quadratic curve, then they will like on a unique cubic curve. In general, N points will determine a unique curve of degree at most (N-1).

No you can't. There is no unique solution for 'x' and 'y'. The equation describes a parabola, and every point on the parabola satisfies the equation.

The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.

It is used for solving a system of linear equations where the number of equations equals the number of variables - and it is known that there is a unique solution.

It means that at least one of the equations can be expressed as a linear combination of some of the other equations. A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations. For example, if you have x + 2y = 3 and 2x + y = 4 Then adding 2 times the first and 3 times the second gives 8x + 7y = 18 This is, therefore, dependent on the other 2. If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.

When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..

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