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3 years ago

How do you know or what indicates to you that the solution set of an equation is all real numbers?

Mathematics

1 answer:

Harrizon [31]3 years ago

3 0

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

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.

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.)

_____

* Non-linear equations may impose limits on the variables, so that "all real numbers" cannot be a solution.

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Musya8 [376]

Answer:

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Step-by-step explanation:

Question says to find the measure of the angle Y.

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We know that sum of all three angles of the triangle is always 180°.

So we can write:

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3∠y=180°

divide both side by 3

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Hence final answer is the measure of angle y is 60 degree.

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3 years ago

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Answer:

Step-by-step explanation:

I first multiplied 490 by 3/7

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As I got 210

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b) For 100 mi of city driving plus 300 mi of highway driving, car A will consume <u>13.475 gallons</u> of gas, while car B will consume <u>12.52 gallons</u> of gas.

<h3>Data and Calculations:</h3><h3>Rating (miles per gallon)</h3>

City Driving Highway Driving

Car A 32 mi/gal 29 mi/gal

Car B 27 mi/gal 34 mi/gal

<h3>Miles of Driving</h3>

City Driving Highway Driving

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b) 100 mi 300 mi

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Learn more about the consumption of gas for driving at brainly.com/question/13244789

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