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What is consistent system with independent equations?
A consistent system with independent equations is one in which there is at least one solution, and the equations do not overlap in their constraints, meaning that no equation can be derived from another. In such a system, the equations represent different planes (or lines in two dimensions), and they intersect at one unique point (in the case of two variables) or along a line (for three variables). This unique intersection indicates that the system has a single solution that satisfies all equations simultaneously.
Why do people call it a system when two lines intersect?
They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.
A system of equations of two or more parallel lines is called a what?
Inconsistent
What is the purpose of the coordination system?
To plot straight and curved lines on it in the form of equations
What the system of linear equation in two variabes which has no solution?
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
What are lines that have equivalent linear equations and overlap at every point when graphed?
coincidental -Lines that share the same solution sets.
What system of equations has no solution?
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
What is true about the lines represented by this system of linear equations?
That they, along with the equations, are invisible!
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.
What is true about a system of two linear equations that has no solution?
The two equations represent parallel lines.
Why do people call it a system when two lines intersect?
They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.
How do you interpret the solution of a system of equations by the corresponding graph?
The solution of a system of equations corresponds to the point where the graphs of the equations intersect. If the equations have one unique point of intersection, that point represents the solution of the system. If the graphs are parallel and do not intersect, the system has no solution. If the graphs overlap and coincide, the system has infinitely many solutions.
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
What types of lines would be the result of an inconsistent system of equation?
If you refer to linear equations, graphed as straight lines, two inconsistent equations would result in two parallel lines.
A system of equations of two or more parallel lines is called a what?
Inconsistent
What is the point at which the lines intersect in a system of linear equations?
The coordinates of the point of intersection represents the solution to the linear equations.
What is the definition of a linear system and how does it relate to solving equations with multiple variables?
A linear system is a set of equations where each equation is linear, meaning it involves variables raised to the power of 1. Solving a linear system involves finding values for the variables that satisfy all the equations simultaneously. This process is used to find solutions to equations with multiple variables by determining where the equations intersect or overlap.
