In what fundamental way does the solution set of a system of linear equations differ from the solution set of a system of linear inequalities? Give examples. Discuss the important implications arising from this difference.

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The solution set of a system of linear equations may consist of just one unique solution or infinitely many solutions. In these cases, we say that the system is consistent. However, in some cases the system may not have a solution at all and we say the system is inconsistent.
Consider a system of linear equations that is consistent. The solution(s) consist of ordered pairs of the form (x, y). Every equation of the system holds only for these ordered pairs of x and y, and for no other.
There are several methods of solving a system of linear equations: Addition, Substitution, Cramer's Rule, Matrix method to name a few. The 2-variable system can be solved graphically also, in which case, the solution is given by the point of intersection of the two lines.

The solution set of a system of inequalities consists of a set of points or a solution space, all the points inside which (and in some cases, points lying on the boundary of the region also) ...

Solution Summary

Solutions of systems of linear equations and linear inequations have been compared, bringing out the similarities and differences between them. Also presented are an example each for the two types.

... intersection of the graphs of the individual inequalities. ... y =4 to the second equation: -3m + 4 ... Systems of Linear Equations: 8.2 Exercises - Solving by Adding. ...

... start, you will be comparing the graphs of linear equations with those of linear inequalities. Consider first a linear equation of the form y = mx + b. 1 ...

... Let us take two lines given by the linear equations in the ... not containing y to the other side of the equation. ... is how we can just see the equations and tell ...

... compared the linear equation graphs and linear inequalities. What are the major differences between the linear equation graph and the linear inequality graph? ...

... 5y ≤ 5 6x + 6y ≤ 60 Graph the system of linear inequalities. ... Then we have the following equation x(1 + 6 ... if it exists, to this system of linear equations: ...

...Linear equations and inequalities are investigated. ... We equate the coefficients of one variable in the two equations and by subtracting one equation from the ...