Answer:
the equation is a tautology, or the system of equations is under-specified
Step-by-step explanation:
By definition, an equation that is a tautology is true for all values of the variable(s). Hence, its solution set is "all real numbers."
One such equation is ...
x = x
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An under-specified system of equations* may also have "all real numbers" as a solution set. For example, two equations in 3 unknowns:
x + y = 3
x + z = 5
The solution set is ...
(x, y, z) = (x, 3-x, 5-x)
Every value of x will give a solution.
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Similarly, a dependent system of equations may have "all real numbers" as a solution. A system is dependent when one or more of the equations can be derived from the others.
For example, adding the equation 2x+y+z=8 to the above set will give 3 equations in 3 unknowns. However, this added equation can be obtained by adding together the two above. It adds nothing that would restrict the solution set.
A system of two equations in two unknowns will be <em>dependent</em> if one of the equations is a constant multiple of the other. For example, x+y=1, 2x+2y=2 has a second equation that is 2 times the first. This set of equations has "all real numbers" as its solution set. (Of course, y = 1-x.)
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* Non-linear equations may impose limits on the variables, so that "all real numbers" cannot be a solution.
