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What is a system of equations that has at least one solution?
a linear equation
A system of two linear equations has exactly one solution if?
The slopes (gradients) of the two equations are different.
If a system of linear equations has exactly one solution then the two lines are what?
perpendicular
What is a unique solution in linear equations?
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.
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
A system of linear equations that has soluton is?
A system of linear equations that has at least one solution is called consistent.
If a system of equations is independent how many soultions will it have?
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.
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
What is a system of equations that has at least one solution?
a linear equation
When does a system of linear equations in two variables have a unique or one solution?
simultaneous equations
What is a system of equations that has a solution of all points on one line?
Linear system
What system of two linear equations in two variables that has exactly one solution?
An independent system has one solution.
What is the solution to a linear equation?
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.
Which number of solutions is not possible for a system of two linear equations?
A system of two linear equations can have either one solution, infinitely many solutions, or no solution at all. However, having exactly two distinct solutions is not possible for such a system, as two linear equations can only intersect at one point (one solution), be parallel (no solution), or be the same line (infinitely many solutions).
A system of two linear equations has exactly one solution if?
The slopes (gradients) of the two equations are different.
If a system of linear equations has exactly one solution then the two lines are what?
perpendicular
What is a unique solution in linear equations?
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.
