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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.
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.
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
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.
When equations of linear systems have different slopes how many solutions does it have?
One solution
What is the purpose and functionality of the MATLAB backslash command in solving linear systems of equations?
The MATLAB backslash command () is used to efficiently solve linear systems of equations by performing matrix division. It calculates the solution to the system of equations by finding the least squares solution or the exact solution depending on the properties of the matrix. This command is particularly useful for solving large systems of linear equations in a fast and accurate manner.
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.
Why are systems of equations important?
Systems of equations are important because they allow us to model and solve real-world problems that involve multiple unknowns. By setting up and solving systems of equations, we can find the values of the variables that satisfy all the equations simultaneously, providing a precise solution to the problem at hand. These systems are widely used in various fields such as physics, engineering, economics, and more, making them a fundamental tool in problem-solving and decision-making.
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.
What is the purpose of the MATLAB backward slash () operator in numerical computations?
The MATLAB backward slash () operator is used for solving systems of linear equations in numerical computations. It helps find the solution to a system of equations by performing matrix division.
What does infinite solutions mean?
Infinite solutions refer to a situation in mathematics, particularly in solving equations or systems of equations, where there are countless solutions that satisfy the given conditions. This typically occurs when the equations are dependent and represent the same geometric entity, such as lines or planes that overlap completely. In practical terms, it means that instead of finding a unique solution, any point along a certain line or surface can be a valid answer.
What are the answers to objective 6a solve systems of equations by graphing?
To solve systems of equations by graphing, you plot each equation on the same coordinate plane and identify the point(s) where the lines intersect. The intersection point(s) represent the solution(s) to the system, indicating the values of the variables that satisfy both equations. If the lines intersect at one point, there is a unique solution; if they are parallel, there is no solution; and if they coincide, there are infinitely many solutions.
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.
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.
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.
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.
