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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.
When does a system of linear equations in two variables have a unique or one solution?
simultaneous equations
What is the solution of an equation with 2 variables x and y?
A linear equation in two variables will not have a single solution. Its solution set is a line in the Cartesian plane. The solution to non-linear equations will depend on the equation.
Can a system of linear equations in two variables have exactly two solutions?
Yes. The easiest case to see where this is true is in the case that the equations are all of degree = 1, which will yield one solution per variable.
What is a system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
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.
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
When does a system of linear equations in two variables have a unique or one solution?
simultaneous equations
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 the solution of an equation with 2 variables x and y?
A linear equation in two variables will not have a single solution. Its solution set is a line in the Cartesian plane. The solution to non-linear equations will depend on the equation.
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.
Can a system of linear equations in two variables have exactly two solutions?
Yes. The easiest case to see where this is true is in the case that the equations are all of degree = 1, which will yield one solution per variable.
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 system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
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 does linear equation in two variable have?
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
