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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
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.
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.
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.
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.
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.
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.
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.
Can systems of equations with the same slopes and different y-intercepts have no solution?
It is a correct statement.
When solving systems of linear equations what does the solution represent?
A single point, at which the lines intercept.
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.
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.
