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Do all rational equations have one solution?
No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.
True or false Are all the techniques and methods used to solve linear equations may be used to solve rational equations?
False. While some techniques used for solving linear equations, such as isolating variables and cross-multiplying, can also be applied to rational equations, not all methods are applicable. Rational equations often require additional steps, such as finding a common denominator and checking for extraneous solutions, due to the presence of variables in the denominator. Thus, the approach to solving rational equations can be more complex than that for linear equations.
How man solutions can a system have?
A system of equations can have three types of solutions: one unique solution, infinitely many solutions, or no solution at all. A unique solution occurs when the equations intersect at a single point, while infinitely many solutions arise when the equations represent the same line or plane. No solution occurs when the equations represent parallel lines or planes that do not intersect. The nature of the solutions depends on the relationships between the equations in the system.
Is it possible for a system of three linear equations to have one solution?
Yes, it is possible for a system of three linear equations to have one solution. This occurs when the three equations represent three planes that intersect at a single point in three-dimensional space. For this to happen, the equations must be independent, meaning no two equations are parallel, and not all three planes are coplanar. If these conditions are met, the system will yield a unique solution.
Does every pair of linear simultaneous equations have a unique solution?
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
Do all rational numbers have single solution?
Numbers are numbers, not questions or equations. They do not have solutions.
Do all rational equations have an single solution?
yes they do except for the one on your test that is worth he most marks
Do all rational equations have one solution?
No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.
What is a system of linear equations?
A system of linear equations determines a line on the xy-plane. The solution to a linear set must satisfy all equations. The solution set is the intersection of x and y, and is either a line, a single point, or the empty set.
What is the difference with equations with integers and equations with rational numbers?
It is a trivial difference. If you multiply every term in the equation with rational numbers by the common multiple of all the rational numbers then you will have an equation with integers.
True or false Are all the techniques and methods used to solve linear equations may be used to solve rational equations?
False. While some techniques used for solving linear equations, such as isolating variables and cross-multiplying, can also be applied to rational equations, not all methods are applicable. Rational equations often require additional steps, such as finding a common denominator and checking for extraneous solutions, due to the presence of variables in the denominator. Thus, the approach to solving rational equations can be more complex than that for linear equations.
How man solutions can a system have?
A system of equations can have three types of solutions: one unique solution, infinitely many solutions, or no solution at all. A unique solution occurs when the equations intersect at a single point, while infinitely many solutions arise when the equations represent the same line or plane. No solution occurs when the equations represent parallel lines or planes that do not intersect. The nature of the solutions depends on the relationships between the equations in the system.
Is it possible for a system of three linear equations to have one solution?
Yes, it is possible for a system of three linear equations to have one solution. This occurs when the three equations represent three planes that intersect at a single point in three-dimensional space. For this to happen, the equations must be independent, meaning no two equations are parallel, and not all three planes are coplanar. If these conditions are met, the system will yield a unique solution.
Does every pair of linear simultaneous equations have a unique solution?
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
Is it possible to have a system of equations that has more than one solution?
Yes, a system of equations can have more than one solution if the equations represent the same line or plane in a geometric sense. In such cases, there are infinitely many solutions that satisfy all equations simultaneously. This typically occurs in systems of linear equations where the equations are dependent. Conversely, if the equations are independent, the system will either have a unique solution or no solution at all.
What is an ordered pair that makes all equations in a system true?
That would be the "solution" to the set of equations.
Which best describes a system of equations that has no solution?
An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.
