It means you performed an operation on the system which was not invertible. This allowed you to come to a solution but that solution is not correct since it is not a proper biconditional relations. That is, you can solve it in terms of p->q but not the reverse (since the inverse operation is not possible).
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
The number of solutions to a nonlinear system of equations can vary widely depending on the specific equations involved. Such systems can have no solutions, a unique solution, or multiple solutions. The behavior is influenced by the nature of the equations, their intersections, and the dimensions of the variables involved. To determine the exact number of solutions, one typically needs to analyze the equations using methods such as graphical analysis, algebraic manipulation, or numerical techniques.
The number of solutions to a system of nonlinear equations can vary widely depending on the specific equations involved. There can be zero, one, multiple, or even infinitely many solutions. The nature of the equations, their degree, and how they intersect in their graphical representations all influence the solution set. Additionally, some systems may have complex solutions, further complicating the count.
isolate
Two nonlinear equations can have zero, one, or multiple solutions, depending on their specific forms and how they intersect in the coordinate system. In some cases, they may intersect at discrete points, while in others, they might not intersect at all. Additionally, there can be scenarios where the equations are tangent to each other, resulting in a single solution. The nature of the solutions is influenced by the shapes of the curves represented by the equations.
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
2
The number of solutions to a nonlinear system of equations can vary widely depending on the specific equations involved. Such systems can have no solutions, a unique solution, or multiple solutions. The behavior is influenced by the nature of the equations, their intersections, and the dimensions of the variables involved. To determine the exact number of solutions, one typically needs to analyze the equations using methods such as graphical analysis, algebraic manipulation, or numerical techniques.
In general, a system of non-linear equations cannot be solved by substitutions.
The number of solutions to a system of nonlinear equations can vary widely depending on the specific equations involved. There can be zero, one, multiple, or even infinitely many solutions. The nature of the equations, their degree, and how they intersect in their graphical representations all influence the solution set. Additionally, some systems may have complex solutions, further complicating the count.
isolate
Two nonlinear equations can have zero, one, or multiple solutions, depending on their specific forms and how they intersect in the coordinate system. In some cases, they may intersect at discrete points, while in others, they might not intersect at all. Additionally, there can be scenarios where the equations are tangent to each other, resulting in a single solution. The nature of the solutions is influenced by the shapes of the curves represented by the equations.
Isolating a variable in one of the equations.
A system of equations means that there are more than one equations. The answer depends on the exact function(s).
there is no linear equations that has no solution every problem has a solution
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.
A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.