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Q: Is it possible for a system of three linear equations to have one solution?

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there is no linear equations that has no solution every problem has a solution

A system of linear equations that has at least one solution is called consistent.

A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.

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.

simultaneous equations

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there is no linear equations that has no solution every problem has a solution

The solution of a system of linear equations is a pair of values that make both of the equations true.

It is a system of linear equations which does not have a solution.

A system of linear equations that has at least one solution is called consistent.

A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.

A system of linear equations can only have: no solution, one solution, or infinitely many solutions.

one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel

Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.

The coordinates of the point of intersection represents the solution to the linear equations.

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.

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.