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What does it mean to be a solution to a system of equations?
basically it means an answer for a multiplication problem
What is a system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
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 graphing how is the solution found?
The solution is the coordinates of the point where the graphs of the equations intersect.
Does the system of equations have a common solution?
Not necessarily.
What does it mean to be a solution to a system of equations?
basically it means an answer for a multiplication problem
What is a system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
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.
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
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.
Solving the system of equations by graphing?
Solving a system of equations by graphing involves plotting the equations on the same coordinate plane and finding the point(s) where the graphs intersect, which represents the solution(s) to the system. Each equation corresponds to a line on the graph, and the intersection point(s) are where the x and y values satisfy both equations simultaneously. This method is visually intuitive but may not always provide precise solutions, especially when dealing with non-linear equations or when the intersection point is not easily identifiable due to the scale or nature of the graphs.
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 interpret the solution of a system of equations by the corresponding graph?
The solution of a system of equations corresponds to the point where the graphs of the equations intersect. If the equations have one unique point of intersection, that point represents the solution of the system. If the graphs are parallel and do not intersect, the system has no solution. If the graphs overlap and coincide, the system has infinitely many solutions.
Is (1 10) a solution to this system of equations?
No because there are no equations there to choose from.
When solving a system of equations by graphing how is the solution found?
The solution is the coordinates of the point where the graphs of the equations intersect.
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.
