# General Solution-Three variables-Two Equations

• mikael27
In summary, a general solution for a system of equations with three variables and two equations is an expression that represents all possible solutions to the system. It can be found by using elimination or substitution methods to eliminate one variable and solve for the remaining two variables, then expressing the remaining two variables in terms of a third variable. A system of equations with three variables and two equations can only have one general solution, as the two equations form constraints that limit the possible values for all three variables. A general solution differs from a particular solution in that it represents all possible solutions while a particular solution is a specific set of values. It is also possible for a system of equations with three variables and two equations to have no general solution, which occurs when the equations
mikael27

## Homework Statement

Find the general solution of the following set of equations:

u − w + y = 1
u + w + 2y = 0

## The Attempt at a Solution

I know that the solution is in this form (u,w,y)= (a,b,c) + k*(d,e,f)

Can you please explain me how i am going to find it?

hi mikael27!

there are several ways to do this

one is to see that each equation represents a plane (in ordinary 3D space)

so their intersection is a line

how would you find the direction of that line?

## 1. What is a general solution for a system of equations with three variables and two equations?

A general solution for a system of equations with three variables and two equations is an expression that represents all possible solutions to the system. It includes all values that satisfy both equations simultaneously.

## 2. How do you find a general solution for a system of equations with three variables and two equations?

To find a general solution for a system of equations with three variables and two equations, you can use elimination or substitution methods to eliminate one variable and solve for the remaining two variables. Then, you can express the remaining two variables in terms of a third variable, which represents all possible solutions.

## 3. Can a system of equations with three variables and two equations have more than one general solution?

No, a system of equations with three variables and two equations can only have one general solution. This is because the two equations form a set of constraints that limit the possible values for all three variables. Therefore, the general solution represents the only set of values that satisfy both equations.

## 4. How is a general solution different from a particular solution for a system of equations with three variables and two equations?

A general solution represents all possible solutions to a system of equations with three variables and two equations, while a particular solution represents a specific set of values that satisfies both equations. A general solution is expressed in terms of one variable, while a particular solution includes specific values for all three variables.

## 5. Can a system of equations with three variables and two equations have no general solution?

Yes, it is possible for a system of equations with three variables and two equations to have no general solution. This happens when the two equations are inconsistent, meaning they have no common solutions. In this case, the system has no solution at all, and there is no general solution for the system.

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