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Do all rational equations have a single solution?
Not all rational equations have a single solution but can have more than one because of having polynomials. All rational equations do have solutions that cannot fulfill the answer.
Do all rational numbers have single solution?
Numbers are numbers, not questions or equations. They do not have solutions.
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.
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.
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.
What is the concept of graphing system of equations?
You take each equation individually and then, on a graph, show all the points whose coordinates satisfy the equation. The solution to the system of equations (if one exists) consists of the intersection of all the sets of points for each single equation.
What are the three types of outcomes for linear equations?
All the lines meet at one point: a single solution. All the lines are the same: infinitely many solutions. At least one of the lines does not pass through the point of intersection of the others: no solution.
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.
How do you check a solution to a system of equations?
Put the values that you find (as the solution) back into one (or more) of the original equations and evaluate them. If they remain true then the solution checks out. If one equation does not contain all the variables involved in the system, you may have to repeat with another of the original equations.
