Answer the following in full sentences What is a system of l

Answer the following in full sentences. What is a system of linear equations? What is the solution of a system of linear equations? When is it easier to use the addition method rather than the substitution method to solve a system of equations? Answer the following in full sentences. What is a system of linear equations in three variables? Describe in general terms how to solve a system in three variables. Answer the following using full sentences. What is a system of nonlinear equations? Provide an example with your description (you may illustrate your example with a graph of the system). Write a system consisting of the equations of two circles for which there is no solution. Draw an accompanying graph.

Solution

A system of equations is a set of equations with the same variables.They can used to solve real world problems. If the equations are all linear, then you have a system of linear equations.To solve a system of equations, you need to figure out the variable values that solve all the equations involved. It can be two variable or more varibale system of equations:

3x +y = 2 ; 2x + 5y = 4 ---- ( 2variable)

3x + y + 2z = 1 ; 5x -2 y + 9z = 8 ; 4x + 5y + 4z = -9 ----( 3varaible)

Solution Linear equations: A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied.

Addition method is better than substitution method :Substitution is the preferred method for 2 equations in 2 unknowns. The constants are unimportant other than having a non-zero determinant.

However it is easier to make any coeffencient equal in two equations eleminate one varible.Whereas in susbstitution it is cumbersome to the airthmetic operations and chances of error are high.