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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.
What is a inconsistent line?
its a system of equations, with no solution
Does the system of equations have a common solution?
Not necessarily.
