Q: What is a system of linear equations that has no solution?

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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.

simultaneous equations

Linear system

A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.

Related questions

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.

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.

The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.

A system of linear equations determines a line on the xy-plane. The solution to a linear set must satisfy all equations. The solution set is the intersection of x and y, and is either a line, a single point, or the empty set.

simultaneous equations

a linear equation