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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.
Explain why a system of linear equations cannot have exactly two solutions?
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What does it means if there are an infinite number of solutions to a system of equations?
In simple terms all that it means that there are more solutions than you can count!If the equations are all linear, some possibilities are given below (some are equivalent statements):there are fewer equations than variablesthe matrix of coefficients is singularthe matrix of coefficients cannot be invertedone of the equations is a linear combination of the others
Can a system of linear equations in two variables have infinitely solutions?
Yes.
Why Two dependent simultaneous linear equations have infinite solutions?
Two dependent linear equations are effectively the same equation - with their coefficients scaled up or down.
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.
Explain why a system of linear equations cannot have exactly two solutions?
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There is a system of linear equations with exactly two solutions is it true or false?
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
Can a system of two linear equations have exactly two solutions?
Yes, a system can, in fact, have exactly two solutions.
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.
Can a system of two linear equations in two variables have 3 solutions?
No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions
What are inifintly equations?
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.
What are linear equations with the same solutions called?
They are called simultaneous equations.
How do you order linear equations?
Equations cannot be ordered.
How many solutions does the system of linear equations shown have?
As there is no system of equations shown, there are zero solutions.
How many possible solutions can a system of two linear equations in two unknowns have?
A system of two linear equations in two unknowns can have three possible types of solutions: exactly one solution (when the lines intersect at a single point), no solutions (when the lines are parallel and never intersect), or infinitely many solutions (when the two equations represent the same line). Thus, there are three potential outcomes for such a system.
What does it mean for a system of linear equations to have no solutions?
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
