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The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions.
With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
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If a system of equations is inconsitient how many solutions will it have?
If a system of equations is inconsistent, there are no solutions.
What is inconsistent equation?
An inconsistent equation (or system of equations) is one that has no possible solutions.
How many solutions does the system of linear equations shown have?
As there is no system of equations shown, there are zero solutions.
What are the possible solutions for a pair of linear equation?
Any system of linear equations can have the following number of solutions: 0 if the system is inconsistent (one of the equations degenerates to 0=1) 1 if the system is linearly independent infinity if the system has free variables and is not inconsistent.
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.
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.
If a dependent system of equations is solved how many solutions will there be?
if a dependent system of equation is solved, how many solutions will there be?
How many solutions does an consistent and dependent system of equations have?
It has more than one solutions.
How many solutions does an inconsistent equation have?
An inconsistent equation (or system of equations) is one that has no possible solutions. That is precisely why we call it inconsistent; there is no solution set that can be substituted for its variable or variables that will make the equation (or system) true.
Can a system of two linear equations have exactly two solutions?
Yes, a system can, in fact, have exactly two solutions.
When a system of equations has one or more solutions it is called?
Consistent.
