# Solving systems of equations

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22. Feb 2016
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### Solving systems of equations

• 1. SOLVING SYSTEMS OF EQUATIONS PROJECT BY HIND ALAWADI SHAMMA HASSAN, MAHRA ABDULLATIF, MARYAM ADEL, ALIA
• 2. Introduction: • Systems, 2 x 2 in this case, are when you have 2 equations and 2 unknowns (letters). Here's an example: • x + y = 3 • x - 2y = 0 • The goal is to find an x guy and a y guy that work in both equations. • I'll show you three different ways to solve these. • The first method is graphing • The second method is substitution • The third method is elimination
• 3. Objectives: •Solve systems of linear equations by: 1. Graphing 2. Substitution 3. Elimination •Solve systems of inequalities
• 4. Definitions: • System of equations : is a set or collection of equations that you deal with all together at once • System of inequalities: is a set of two or more inequalities with the same variables • Consistent: has a solution 1. Independent = 1 solution 2. Dependent = infinite solutions • Inconsistent: no solution
• 5. How to solve a system of equations? Y=2x+3 Y=11-2x X Y=2X+3 0 2.0+3=3 1 2.1+3=5 0 1 Y=11-2x 11-2.0=11 11-2.1= 9 (0,3) (1,5) (0,11) (1,9)
• 6. (0,3) (1,5) (0,11) (1,9) Approximately: (2,7)
• 7. How to solve a system of equations? Y=2x+3 Y=11-2x 2x+3=11-2x 2x+2x=11-3 4x=8 4x(/4)=8(/4) X=2 Y=2.(2)+3 Y=4+3 Y=7 Y=11-2x Y=11-2.(2) Y=11-4 Y=7
• 8. Y=2x+3 Y=11-2x How to solve a system of equations? Y=2x+3 - Y=-2x+11 __________ 0=4x-8 =4x-8 8=4x 8(/4)=4x(/4) 2=x Y=2.(2)+3 Y=4+3 Y=7 Y=11-2x Y=11-2.(2) Y=11-4 Y=7
• 9. How to solve a system of inequalities? 6x-3y<-9 -3y<-9-6x Y<3+2x 4x-3y>=1 -3y>=1-4x Y>=-0.33+1.33x
• 10. Real life application • Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold? Let x = small pitcher y = large pitcher 2x + y = 8 y - x = 2 2x + y = 8 -x + y = 2 subtract: 3x = 6 x = 2 The small pitcher holds 2 cups of water. 2(2) + y = 8 4 + y = 8 y = 4 The large pitcher holds 4 cups of water.
• 11. Real life application • A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? Let x = T/F questions Let y = Multiple Choice questions x + y = 20 3x + 11y = 100 x + y = 20 3x + 11y = 100 3(x + y = 20) 3x + 11 y = 100 3x + 3y = 60 3x + 11y = 100 -8y = -40 8y = 40 y = 5 There are 5 multiple choice questions. x + 5 = 20 x = 15 There are 15 T/F questions.
• 12. Benefits from the lesson •You could determine variables in two equations in real life •You are able to solve using graphing, substitution and elimination •You are able to estimate values of variables by solving a system of inequalities
• 13. Resources: • http://www.purplemath.com/modules/syseqgen.htm • http://math.about.com/od/linearequations/tp/Syst_Lin-1.html • http://www.mathwarehouse.com/algebra/linear_equation/systems- of-equation/system-linear-inequality.php • The algebra textbook
• 14. THE END