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How many solutions will a system have if the graph of the solution is coinciding lines?
no solutions
How many solutions will a system have if the graph of the solution is not parallel lines?
infinitely many solutions :)
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.
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.
How can you tell what the solution is from the graph of a system?
To determine the solution of a system from its graph, look for the point where the graphs of the equations intersect. This intersection point represents the values of the variables that satisfy all equations in the system simultaneously. If the graphs do not intersect, the system may have no solution, indicating that the equations are inconsistent. If the graphs overlap entirely, it suggests that there are infinitely many solutions.
How many solutions will a system have if the graph of the solution is intersecting lines?
one solution
How many solutions will a system have if the graph of the solution is coinciding lines?
no solutions
How many solutions will a system have if the graph of the solution is parallel lines?
No Solutions
How many solutions will a system have if the graph of the solution is not parallel lines?
infinitely many solutions :)
Does the graph of a system of equations with different slopes have no solutions?
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
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.
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.
How can you tell what the solution is from the graph of a system?
To determine the solution of a system from its graph, look for the point where the graphs of the equations intersect. This intersection point represents the values of the variables that satisfy all equations in the system simultaneously. If the graphs do not intersect, the system may have no solution, indicating that the equations are inconsistent. If the graphs overlap entirely, it suggests that there are infinitely many 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.
How can you determine whether a system has no solutions by graphing?
If you graph the two functions defined by the two equations of the system, and their graphs are two parallel line, then the system has no solution (there is not a point of intersection).
The solution of a system of equation is?
the solution to a system is where the two lines intersect upon a graph.
When solving a system of equations by graphing you will need to graph the equations on the same?
When solving a system of equations by graphing, you will need to graph the equations on the same coordinate plane. This allows you to visually identify the point where the two lines intersect, which represents the solution to the system. If the lines intersect at a single point, that point is the unique solution; if the lines are parallel, there is no solution; and if they coincide, there are infinitely many solutions.
