System of Linear Equation

SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES bring in the following systems 1. ? ? x ? y ? 8 ? x ? y ? 2 by graphing by commuting by elimination by Cramers rule 2. ? ?2 x ? 5 y ? 9 ? 0 ? x ? 3y ? 1 ? 0 by graphing by substitution by elimination by Cramers rule 3. ? ?4 x ? 5 y ? 7 ? 0 ? 2 x ? 3 y ? 11 ? 0 by graphing by substitution by elimination by Cramers rule CASE 1 intersecting lines independent & consistent m1? m2 CASE 2 mate lines inconsistent m1 = m2 b1 ? b2CASE 3 cooccur lines consistent & dependent m1 = m2 b1 = b2 Classify the following system, whether (a) intersecting, (b) parallel, or (c) coinciding lines 1. ? ? 3 x ? 4 y ? 1 ? 0 ? 3 x ? 4 y ? 2 ? 0 ? 3 x ? 4 y ? 1 ? 0 ? 6 x ? 8 y ? 2 ? 0 Solve the following systems in three variables 1. ?3 x ? 4 y ? z ? 1 2. ? x ? y ? 2 ? ? x ? 4 y ? 3z ? 3 ? 3 x ? 2 y ? 2 z ? 0 ? ________ ? ? 3 y ? z ? 1 ? x ? 2 z ? 7 ? 2. ? ________ 3. ? ?2 x ? 5 y ? 1 ? 0 ? 5 ? x ? 2 y ? 2 ? 0 ? ?2 x ? ? 1 ? 4 x ? 2 y ? 3 ? x ? 2 y ? 1 ? 0 ? 2 x ? y ? 1 ________ 4. ? ________ 5. ? ________ ?1 ? x ? ? Solve ? ?1 ? ?x ? 2 ? 3 y 3 ? 2 y Problem solving Form a system of equations from the problems given below. A) (MIXTURE PROBLEM 1) How many pounds of a 35% salt antecedent and a 14% salt solution should be combined so that a 50 pounds of a 20% solution is obtained? B) (UNIFORM MOTION) Two motorists start at the same time from two places 128 km apart and drive toward individually other.One drives 10kph than the other. If they met after 48 minutes (that is, 4/5 hr), find the average speed of each. C) A dietician is preparing a repast consisting of foods A, B, and C as shown in the table below. Fat Protein Carbohydrate If the meal must provide exactly 24 units of fat, 25 Food A 3 2 4 units of protein, and 21 units of carbohydrate, how Food B 2 3 1 many ounces of each food should be used? Food C 3 3 2