INTRODUCTION TO SYSTEMS OF LINEAR EQUATIONS II

CONTINUATION...

A System of m linear equations in n variables is a set of m equations, each of which is linear in the same n variables

a₁₁x₁ + a₁₂x₂ + a₁₃x₃ + . . . + a_1nx_n = b₁
a₂₁x₁ + a₂₂x₂ + a₂₃x₃ + . . . + a_2nx_n = b₂
a₃₁x₁ + a₃₂x₂ + a₃₃x₃ + . . . + a_3nx_n = b₃

a_m1x₁ + a_m2x₂ + a_m3x₃ + . . . + a_mnx_n = b_m

A system of linear equations is said to be Consistent if it has at least one solution and Inconsistent if it has no solution

EXAMPLES OF SYSTEMS OF TWO EQUATIONS IN TWO VARIABLES
Solve each system of linear equations 
A.) x + y = 3 and  x – y = -1 

The system has exactly one solution ( 1 , 2 ).The solution can be obtained by adding the two equations.*It is Consistent Independent since it has exactly one solution
B.) x + y = 3 and 2x + 2y = 6

The system has an infinite number of solutions. A parametric representation is shown as x = 3 – v, y = v, v is an element of all real numbers.*It is Consistent Dependent since it has an infinite number of solutions

C.) x + y = 3 and x + y = 1

The system has no solution because it is impossible for the sum of two numbers to be 1 and 3 simultaneously.*It is Inconsistent since it has no solution

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