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.
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.
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.
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 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.
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..
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.
A system of linear equations that has at least one solution is called consistent.
It is a system of linear equations which does not have a solution.
A system of linear equations can only have: no solution, one solution, or 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.
The coordinates of the point of intersection represents the solution to the linear equations.
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.
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many 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.
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 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.
It can happen. Then there is no solution!It can happen. Then there is no solution!It can happen. Then there is no solution!It can happen. Then there is no solution!
The two equations represent parallel lines.
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 set of equations is inconsistent, if its solution set is empty.