System of three equations x^2 + (xz) - y - z = 0

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In summary, a system of equations is a set of related equations that must be solved together to find a common solution. A system of three equations can have zero, one, or infinitely many solutions, depending on the specific equations and their relationship. The solution to a system of equations is represented as a set of values that satisfy all of the equations. A system of equations can have no solution if the equations are inconsistent, and it can have infinitely many solutions if the equations are dependent.
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Find x, y, z solving all the three equations:

y^2 + (y*x) - z - x = 0z^2 + (z*y) - x - y = 0x^2 + (x*z) - y - z = 0I would be very grateful!
 
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x = y = z = 1
 

FAQ: System of three equations x^2 + (xz) - y - z = 0

What does the term "system of equations" mean in this context?

A system of equations refers to a set of equations that are related and must be solved together to find a common solution.

How many solutions can a system of three equations have?

A system of three equations can have zero, one, or infinitely many solutions. This depends on the specific equations and their relationship to each other.

How is the solution to a system of equations represented?

The solution to a system of equations is represented as a set of values that satisfy all of the equations in the system. In this case, it would be the values of x, y, and z that make the equation x^2 + (xz) - y - z = 0 true.

Can a system of equations have no solution?

Yes, a system of equations can have no solution if the equations are inconsistent and cannot be satisfied by any value of the variables.

Can a system of equations have more than one solution?

Yes, a system of equations can have infinitely many solutions if the equations are dependent and have an infinite number of values for the variables that satisfy them.

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