LrChVIISILinearInequalitiesTwoVariables

LrChVIISILinearInequalitiesTwoVariables - Qualitative...

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Unformatted text preview: Qualitative Choice Analysis Workshop 1 Econometrics Laboratory 7.1 Linear Inequalities in Two Variables Dr. Raja Mohammad Latif We will geometrically represent the solution of a linear inequality in two variables and will extend this representation to a system of linear inequalities . Math 131 (052: Feb 12-June10, 2006) 3 0.1 7.1. Linear Inequalities in Two Variables Many applications of mathematics involve systems of inequal- ities rather than systems of equations. A graph is often the most convenient way to represent the solutions of a system of linear inequalities in two variables. In this section we discuss techniques for graphing both a single linear inequality in two variables and a system of linear inequalities in two variables. A line divides the plane into two halves called half-planes . A vertical line divides it into left and right half-plane ; Left half pl & y ane " " P j Right half & plane L H j L j Right half & plane E A j A j Right half & plane & & & - j- & - j- & &! x T L j N j Right half & plane F j E j Right half & plane Left half pl & j ane # Right half & plane A nonvertical line divides it into upper and lower half planes. Mathematical Sciences, KFUPM Math 131 (052: Feb 12-June10, 2006) 4 U P R % U pp er " H F & L h a l f j P & H P p la n e j & L O R & H F P L & & & & j & & & &! x U H & L j lo w e r P & H F j h a l f . P L N j p l an e ========================= y = x & 2 To investigate the half-planes determined by a linear equation such as y & x = & 2 , we rewrite the equation as y = x & 2 : For any given value of x; there is exactly one value for y such that ( x; y ) lies on the line. The four inequalities formed from y = x & 2 by replacing the = sign by >; ¡ ; <; and ¢ ; respectively, are y > x & 2 y ¡ x & 2 y < x & 2 y ¢ x & 2 The graph of each is a half-plane, excluding the boundary Mathematical Sciences, KFUPM Math 131 (052: Feb 12-June10, 2006) 5 line for < and > , and including the boundary line for & and ¡ : Indicate the half-planes with small arrows on the grapf of y = x ¢ 2 and then graph as shaded region....
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LrChVIISILinearInequalitiesTwoVariables - Qualitative...

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