Determining whether system of equations have a solution

Thread starter katerine
Start date Jan 19, 2011
Tags

System System of equations

In summary, to solve a system of equations, you can use methods such as substitution, elimination, or graphing to find the values of the variables that satisfy all of the equations. A system of equations has a solution when the equations intersect at a point, but has no solution when the equations do not intersect or when they are inconsistent with each other. A system of equations can have more than one solution if the equations represent the same line or intersect at multiple points. The main difference between a system of equations and a single equation is that a system of equations has multiple variables and can have multiple solutions, while a single equation typically has one variable and only one solution.

Jan 19, 2011

katerine

how know how to do tis question
determine the value a
for which the resulting linear system has
i) no solution
ii)a unique solution
iii)infinitely many solution

x+y+z=3
x+2y+z=3
x+y+(a^2-8)z=a

Physics news on Phys.org

Jan 19, 2011

Fredrik

Staff Emeritus

Science Advisor

Gold Member

katerine said:

x+y+z=3
x+2y+z=3

What do these two equations tell you about x,y and z?

1. How do you solve a system of equations?

To solve a system of equations, you can use various methods such as substitution, elimination, or graphing. These methods involve manipulating the equations to isolate a variable and then substitute its value into the other equation(s) to find the solution.

2. How do you know if a system of equations has a solution?

A system of equations has a solution when the equations intersect at a point, meaning that the values of the variables will satisfy both equations. This can be seen visually by graphing the equations or algebraically by solving for the variables.

3. What does it mean if a system of equations has no solution?

If a system of equations has no solution, it means that the equations do not intersect and there is no single point that satisfies both equations. This could happen when the equations represent parallel lines or when they are inconsistent with each other.

4. Can a system of equations have more than one solution?

Yes, a system of equations can have more than one solution. This happens when the equations represent the same line or when they intersect at more than one point. In these cases, any value that satisfies both equations is considered a solution.

5. What is the difference between a system of equations and a single equation?

A single equation typically has one variable and can have only one solution, while a system of equations has multiple variables and can have multiple solutions. In a system of equations, the solutions must satisfy all of the equations, while in a single equation, there is only one solution that satisfies the equation.