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How are the graphs of systems of linear equations and inequalities related to their solutions?
The graphs of systems of linear equations represent the relationships between variables, with each line corresponding to an equation. The point(s) where the lines intersect indicate the solution(s) to the system, showing where the equations are satisfied simultaneously. For systems of linear inequalities, the graphs display shaded regions that represent all possible solutions that satisfy the inequalities; the intersection of these regions highlights the feasible solutions. Therefore, both the graphs and their intersections are crucial for understanding the solutions to the systems.
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Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Do solutions to systems of linear inequalities need to satify both inequalities?
If it is joined by an "and" it does. If it is joined by an "or" it does not.
How many solution sets do systems of linear inequalities have. Must solutions to systems of linear inequalities satisfy both inequalities. In what case might they not?
There is only one solution set. Depending on the inequalities, the set can be empty, have a finite number of solutions, or have an infinite number of solutions. In all cases, there is only one solution set.
How many solutions do systems of linear inequalities have?
They can have none, one or infinitely many.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Do solutions to systems of linear inequalities need to satify both inequalities?
If it is joined by an "and" it does. If it is joined by an "or" it does not.
How many solution sets do systems of linear inequalities have. Must solutions to systems of linear inequalities satisfy both inequalities. In what case might they not?
There is only one solution set. Depending on the inequalities, the set can be empty, have a finite number of solutions, or have an infinite number of solutions. In all cases, there is only one solution set.
Systems of equations have one solution?
Systems of equations can have just about any number of solutions: zero, one, two, etc., or even infinitely many solutions.
How many solutions do systems of linear inequalities have?
They can have none, one or infinitely many.
Are there more potential solutions to systems of inequalities in a half-plane or in the entire plane?
There are more solutions in a half plane
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
How solve systems of equations and inequalities using elimination?
To solve systems of equations using elimination, first align the equations and manipulate them to eliminate one variable. This is often done by multiplying one or both equations by suitable constants so that the coefficients of one variable are opposites. After adding or subtracting the equations, solve for the remaining variable, then substitute back to find the other variable. For inequalities, the same elimination process applies, but focus on determining the range of values that satisfy the inequalities.
Why is it important to know various techniques for solving systems of equations and inequalities?
It is important to know several techniques for solving equations and inequalities because one may work better than another in a particular situation.
What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
When equations of linear systems have different slopes how many solutions does it have?
One solution
