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

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Thread starter Anita6363
Start date Oct 31, 2018
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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.

Oct 31, 2018

Anita6363

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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Oct 31, 2018

Wilmer

x = y = z = 1

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

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.