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..
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.
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.
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.
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
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.
Cramer's rule is applied to obtain the solution when a system of n linear equations in n variables has a unique solution.
The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.
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.
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.
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
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.
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.
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.
a1/a2 is not equal to b1/b2
It is a set of equations, which is also called a system of equations. There may be no solution, a single (unique) solution or more than one - including infinitely many.
Linear equations take the form y= mx+b wherem is the slope [rise(y)/run(x) on a graph]x is the x-value any point on the graphy is the y-value of any point on the graphb is the y-intercept on the graphLinear equations take the form a1x1 + a2x2 + a3x3 + ... + anxn + an+1 = 0Each ai represents a constant, xi a variable.The equation above is linear in n dimensions. In two dimensions, linear equations are typically written ax + by = c. In three dimensions, ax + by + cz = d. After that, the form given above (with the subscripts) is preferred.Any system of n equations and n unknowns may have a unique solution. If two of the equations are multiples of each other, the solution set will not be unique, but represent a line, plane, or subspace. It is also possible the system may have no solution, such as the following:5x + 10y = 55x + 10y = 20This system represents two parallel lines--there is no solution.
x = 3, y = 9 is one solution from infinite number of solutions.to 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)
There is no such pair. The solution to equation 1 and equation 2 is x = 1, y = 1. The solution to equation 2 and equation 3 is x = 1, y = 1. And the solution to equation 1 and equation 3 is any point on the line 3x + 2y = 5 - an infinite number of solutions. The fact that the determinant for equations 1 and 3 is zero (or that they are not independent) does not mean that there is no solution. It means that there is no UNIQUE solution. In this particular case, the two equations are equivalent and so have an infinite number of solutions.
There are four unknown variables and only three linear equations so there is not a unique solution. All you can do is to rearrange the four variables so that three of them can be expressed in terms of the fourth. For example: In terms of c, a = 6 - c/2 b = a - c = 6 - 3c/2 d = c
It depends. Partly on the domain over which your system of equations is defined - are they integer solutions? Reals or complex numbers? Are the equations linear or more complicated?In any case, there can be none, one or many - including infinitely many.If the system is inconsistent ega + b = 3a + b = 2then there are no solutions.If the system is incomplete (the relevant matrix is singular), you have an infinite number:a + b + c = 1a + 2b + 3c = 2has an infinite number of solutions.A set of n independent linear equations in n unknowns will have a unique solution.A single equation such as (a-2)2 + (b-3)2 + (c-7.5)2 = 0has a unique real-number solution since each on the brackets MUST be zero.
You don't need ANY factor. To find a unique solution, or a few, you would usually need to have as many equations as you have variables.
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.
Roughly speaking, to get a unique solution - or at least, a limited number of solutions - if you have 3 variables, you need 3 equations, not just 2. With the two equations, you can get a relationship between the three variables, but not a unique value for a, b, and c. To get the general relationship, solve both equations for "c", replace one in the other, and solve the resulting equation for "a" to get the relationship between the variables "a" and "b". Then, for any valid combination of values for "a" and "b", use the simpler of the original equations (a + b + c = 24) to get the corresponding value for "c".