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Systems of equations can have just about any number of solutions: zero, one, two, etc., or even infinitely many solutions.
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When equations of linear systems have different slopes how many solutions does it have?
One solution
Which of the following systems of equations has no solution?
If they are quadratic equations then if their discriminant is less than zero then they have no solutions
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.
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.
When solving systems of linear equations what does the solution represent?
A single point, at which the lines intercept.
When equations of linear systems have different slopes how many solutions does it have?
One solution
Which of the following systems of equations has no solution?
If they are quadratic equations then if their discriminant is less than zero then they have no solutions
What is a systems of equations that has the same solution set as another system?
They are called equivalent systems.
Why are systems of equations important?
A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique 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.
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.
When solving systems of linear equations what does the solution represent?
A single point, at which the lines intercept.
Can systems of equations with the same slopes and different y-intercepts have no solution?
It is a correct statement.
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 does the solution represent when a system of equations has a single solution?
The graphs of the two equations have only one intersection point.
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.
When solving systems of linear equation's when would you get no solution as an answer?
You get no solution if the lines representing the graphs of both equations have the same slope, i.e. they're parallel. "No solution" is NOT an answer.
