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What is true about a system of two linear equations that has no solution?
The two equations represent parallel lines.
How are linear inequalities different from linear equations?
A linear equation represents a line. A linear inequality represents part of the space on one side (or the other) of the line defined by the corresponding equation.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
How do you judge whether an equation has solutions by looking at it in standard form?
If you're talking about two linear equations, make sure they are not parallel. If you're talking about quadratics, make sure that b2-4ac is not negative.
What is the classification of a system of equations?
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
What is true about a system of two linear equations that has no solution?
The two equations represent parallel lines.
How can you tell linear equations are parallel?
Equations are never parallel, but their graphs may be. -- Write both equations in "standard" form [ y = mx + b ] -- The graphs of the two equations are parallel if 'm' is the same number in both of them.
How do you identify two linear equations that are parallel using slopes of two lines?
Two linear equations that are parallel with have the sameslope, or the m value in y = mx + b will be the same.For example, y = 3x + 5 is parallel to y = 3x - 6
If a system of linear equations has no solution then the graph of the two equationsmust be what kind of line?
parallel
How are linear inequalities different from linear equations?
A linear equation represents a line. A linear inequality represents part of the space on one side (or the other) of the line defined by the corresponding equation.
Is it possible for a system of linear equations to have zero solutions?
Yes, a system of linear equations can have zero solutions, which is known as an inconsistent system. This occurs when the equations represent parallel lines that never intersect, meaning there is no point that satisfies all equations simultaneously. A common example is the system represented by the equations (y = 2x + 1) and (y = 2x - 3), which are parallel and thus have no solutions.
Can a system of linear equations have no solution?
Yes, a system of linear equations can have no solution, which occurs when the equations are inconsistent. This typically happens when the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts. As a result, they never intersect, indicating that there are no values for the variables that satisfy all equations simultaneously.
What are the common characteristic between simultaneous linear equations in 2 unknowns which have no solutions?
The coefficients and constant in one of the equations are a multiple of the corresponding coefficients and constant in the other equation.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
What makes two linear equations either parallel or perpendicular to each other?
Depending on the value of the slope or gradient if its the same then they are parallel if its a reciprocal then they are perpendicular.
Are linear equations and functions different?
All linear equations are functions but not all functions are linear equations.
How do you judge whether an equation has solutions by looking at it in standard form?
If you're talking about two linear equations, make sure they are not parallel. If you're talking about quadratics, make sure that b2-4ac is not negative.
