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When is it possible for an ordered pair to be the solution of more than one equation?
Always. Every ordered pair is the solution to infinitely many equations.
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.
When solving a system of equations by elimination you find what?
You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.
What does the solution represent when a system of equations has a single solution?
The graphs of the two equations have only one intersection point.
What is numerical solutions of nonlinear equations?
Linear equations, if they have a solution, can be solved analytically. On the other hand, it may not always be possible to find a solution to nonlinear equations. This is where you use various numerical methods (eg Newton-Raphson) to work from one approximate numerical solution to a better solution. This iterative procedure, if properly applied, gives accurate numerical solutions to nonlinear equations. But as mentioned above, they are not arrived at analytically.
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
When is it possible for an ordered pair to be the solution of more than one equation?
Always. Every ordered pair is the solution to infinitely many equations.
A system of equations with 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.
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.
When solving a system of equations by elimination you find what?
You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.
What does the solution represent when a system of equations has a single solution?
The graphs of the two equations have only one intersection point.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
What is numerical solutions of nonlinear equations?
Linear equations, if they have a solution, can be solved analytically. On the other hand, it may not always be possible to find a solution to nonlinear equations. This is where you use various numerical methods (eg Newton-Raphson) to work from one approximate numerical solution to a better solution. This iterative procedure, if properly applied, gives accurate numerical solutions to nonlinear equations. But as mentioned above, they are not arrived at analytically.
What are the possible solutions for a system of equations?
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.
When does a system of linear equations in two variables have a unique or one solution?
simultaneous equations
How many of the different kinds of solution sets are possible in two linear equations?
Three different kinds: none, one and infinitely many.
How will a system of equations that has one solution be graphed?
They will be a set of lines meeting at one point - the solution.
