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Assuming that the system is two linear equations of two unknowns, solving by substitution will produce a constant that is equal to a different constant. This is because each equation defines a line and the only way for there to be no intersecting points between the two lines would be for them to be parallel to each other. So that their y=mX+b forms will only differ by their y-intercepts since their slopes will be identical. Setting the mx+b portion of the two equations equal to each other allows us to subtract mx from each side of the equal sign leaving us with the slope intercepts being equal to each other. BUT since the y-intercepts were different, we will arrive at a contradiction.
By the way, solving a system of linear equations and having it produce a constant being equal to itself means that the two lines coincide and have infinitely many solutions.
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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 is a inconsistent line?
its a system of equations, with no solution
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?
Graph both equations on the same graph. Where they intersect is the solution to the system of equations
Determine if the ordered pair y3x 5 yx 9 211 isa solution to the system of equations?
Tell whether the ordered pair (5, -5) is a solution of the system
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.
Must solutions to systems of linear equalities satisfy both equalities?
Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.
