System of Linear Equation

SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES Solve the following systems: 1. ? ? x ? y ? 8 ? x ? y ? 2 by graphing by substitution by elimination by Cramer’s rule 2. ? ?2 x ? 5 y ? 9 ? 0 ? x ? 3y ? 1 ? 0 by graphing by substitution by elimination by Cramer’s rule 3. ? ?4 x ? 5 y ? 7 ? 0 ? 2 x ? 3 y ? 11 ? 0 by graphing by substitution by elimination by Cramer’s rule CASE 1: intersecting lines independent & consistent m1? m2 CASE 2: parallel lines inconsistent m1 = m2 ; b1 ? b2 CASE 3: coinciding 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 solution 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 each 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 meal 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