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.
1
dependent
None, one or infinitely many.
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.
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
As there is no system of equations shown, there are zero solutions.
1
dependent
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).
None, one or infinitely many.
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.
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
yes it can . the system may have infinitely many solutions.
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
Yes, a system can, in fact, have exactly two solutions.
A set of equations is inconsistent, if its solution set is empty.