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what- use the slopes and y- intercept of the lines to determine the number of solutions to the system?
consistent dependent
The two lines graphed below are parallel How many solutions are there to the system of equations?
Although there is no graph, the number of solutions is 0.
Can a system of two linear equations have only two or three soltions why or why not?
No. There are none, one or infinitely many solutions. No other value is possible. A system of two linear equation can be represented by two straight lines in space (of 2 or more dimensions). Such lines can be non-intersecting (0 solutions), or they can intersect at one point (1 solution), or they can be coincident (infinitely many solns). Two non-intersecting lines in 2-d space must be parallel but in spaces of 3 or more dimensions they can simply be non-coplanar. For example, imagine you are in a cuboid room. One line is the join of the walls to your left and behind you, the other line is where the floor meets the far wall. These lines are not parallel but they do not meet.
What system of equations has no solution?
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
How does graphing a linear system help you verify the results of solving a linear system algebraically?
You see the point the two lines cross, if they do. This is the solution to the system since it is the values of (x,y) that are on both lines The solution is a sytems is those points, if any, (x,y) that satisfy both equations. That is the same as saying they are on both lines. If you graph the equations, this is the same as saying the points that are in the intersection of the lines. This is why parallel lines represent a system with no solution and if two equations are the same line there is an infinite number of solutions.
How many solutions does this system have?
To determine how many solutions a system has, we need to analyze the equations involved. Typically, a system of linear equations can have one solution (intersecting lines), infinitely many solutions (coincident lines), or no solution (parallel lines). If you provide the specific equations, I can give a more accurate assessment of the number of solutions.
Do graph of a system of parallel lines will have no solutions?
Correct. Unless the parallel lines are coincident, in which case the solution set is the whole line.
Is the system of equations is consistent consistent and coincident or inconsistent?
A system of equations is considered consistent if it has at least one solution, and it is coincident if all solutions are the same line (infinitely many solutions). If the system has no solutions, it is inconsistent. To determine the nature of a specific system, you need to analyze its equations; for example, if two equations represent the same line, it is consistent and coincident, while parallel lines indicate inconsistency.
A system of linear equation in two variables can have how many solutions?
None, one or an infinite number. In graph form, the three correspond to: None = Parallel lines One = Interscting lines Infinite = Coincident lines.
How do you know if a system of linear equations has one solution infinitely many solutions or no solutions?
To determine the number of solutions for a system of linear equations, you can analyze the equations graphically or algebraically. If the lines represented by the equations intersect at a single point, there is one solution. If the lines are parallel and never intersect, there are no solutions. If the lines are coincident (overlap completely), there are infinitely many solutions. Algebraically, this can be assessed using methods like substitution, elimination, or examining the rank of the coefficient matrix relative to the augmented matrix.
How do you know which region of the graph of a system of linear inequalities contains the solutions?
If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.
On a graph the solution of a system of a linear equations will be represented by what?
The set of points the graphed equations have in common. This is usually a single point but the lines can be coincident in which case the solution is a line or they can be parallel in which case there are no solutions to represent.
If a system of linear of linear equations has infinitely many solutions what does this mean about the two lines?
If a system of linear equations has infinitely many solutions, it means that the two lines represented by the equations are coincident, meaning they lie on top of each other. This occurs when both equations represent the same line, indicating they have the same slope and y-intercept. As a result, any point on the line is a solution to the system.
Will The graph of a system equation will intersect at exactly 1 point?
A system of equations will intersect at exactly one point if the equations represent two lines that are neither parallel nor coincident, meaning they have different slopes. In this case, there is a unique solution to the system. If the lines are parallel, they will not intersect at all, and if they are coincident, they will intersect at infinitely many points.
What are the possible solutions to a system of the linear equations and what do they represent graphically?
A system of linear equations can have one solution, infinitely many solutions, or no solution. A single solution occurs when the lines intersect at one point, representing the unique intersection of the two equations. Infinitely many solutions arise when the lines are coincident, meaning they lie on top of each other, representing the same linear relationship. No solution happens when the lines are parallel and never intersect, indicating that there is no set of values that satisfy both equations simultaneously.
what- use the slopes and y- intercepts of he lines to determine the number of solutions to the system?
inconsistent
When you graph a system and all you see is one line how many solutions will the system have?
If you graph a system of two lines and all you see is one line, this means that both lines are the same. Any point on the line is a solution, so the system has an infinite number of solutions.
