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Q: When would there be only four different equations for a set of math mountain numbers?

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There are many different combinations of six numbers, but the sum of those numbers would have to be 24.

There would be no median.

Originally, they were invented to provide solutions to algebraic equations, which would otherwise have no solution. Through the work of Euler, Gauss and others, the usefulness of imaginary and complex numbers in applications of periodic motion and waves was recognized. See related links.

You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.

When talking about a "system of equations", you would normally expect to have two or more equations. It is quite common to have as many equations as you have variables, so in this case you should have two equations.

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No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.

Of course, equations are going to be studied in arithmetic while in elementary school. A different kind of equations will be studied in algebra and calculus in high school.

Lucky Numbers would be different for different people and would vary greatly.

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Equations can have as many variables as you want, however to solve an equation you need as many equations as there are unknowns. E.g. in an equation with x & y as the unknowns you would need two different equations containing x and/or y to solve them

The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.

Then they would not be the same.

Well, I think that means differnet types of math fields. This would mean like arthmitic, equations, complex numbers and so on.

No, chemical equations are balanced by adjusting the coefficients in front of the chemical formulas. Changing the subscripts would alter the actual chemical identities of the substances involved.

There are many different combinations of six numbers, but the sum of those numbers would have to be 24.

There would be no median.

any differential equation would be considered a calculus equations.