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To determine how many solutions a linear system has, we need to analyze the equations involved. A linear system can have one unique solution, infinitely many solutions, or no solution at all. This is usually assessed by examining the coefficients and constants of the equations, as well as using methods like substitution, elimination, or matrix analysis. If the equations are consistent and independent, there is one solution; if they are consistent and dependent, there are infinitely many solutions; and if they are inconsistent, there are no solutions.
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How many solutions does a system of linear equations in three variables have?
1
Can a system of two linear equations have exactly two solutions explain?
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
Why could a system of linear equations have two solutions?
A system of linear equations cannot have two distinct solutions if it is consistent and defined in a Euclidean space. If two linear equations intersect at a single point, they have one solution; if they are parallel, they have no solutions. However, if the equations are dependent, meaning one equation is a multiple of the other, they represent the same line and thus have infinitely many solutions, not just two. Therefore, in standard scenarios, a system of linear equations can either have one solution, no solutions, or infinitely many solutions, but not exactly two.
How many solutions can a system of linear equations with two variables?
None, one or infinitely many.
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.
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 solutions does a system of linear equations in three variables have?
1
If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
Can a linear system have exactly two solutions?
NO! A linear system can only have one solution (the lines intersect at one point), no solution (the lines are parallel), and infinitely many solutions (the lines are equivalent).
How many solutions can a system of linear equations with two variables?
None, one or infinitely many.
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.
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 linear system that has more unknowns than equation be consistent?
yes it can . the system may have infinitely many solutions.
What are the three types of system of linear equations?
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
How many solutions does a system of linear equations have if it is inconsistant?
A set of equations is inconsistent, if its solution set is empty.
Can a system of two linear equations have exactly two solutions?
Yes, a system can, in fact, have exactly two solutions.
