Categories of systems of linear equation.pptx

This presentation is all about the different categories of systems of linear equations in two variables and the different methods of solving it

1. Mathematics 8 With Ma'am Nor

2. Prayer

3. Energizer

4. Review

5. What is the answer?

6. How much is an apple?a bunch of bananas?

7. What is your equation in life?

8. Life + Love = HAPPY Life - Love=LONELY Life = 1/2 HAPPY + 1/2 LONELY 2Life = HAPPY+LONELY 2

9. OBJECTIVES determine the characteristics of the different systems of equation solve systems of equations using different methods

10. If we are to make a mathematical equation out of the picture, what would it be? Let a-cost of an apple b-cost of banana

11. a +a + a = 18 3a= 18 a + b+b =14 a + 2b=14

12. Systems of Linear Equations SIBULAN SCIENCE HS With Ma'am Nor

13. A system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously.

14. Solution of a sytem -ordered pairs that make all the equations true. The solution to a sytem is where the graphs of the system intersect

15. CATEGORIES OF A SYSTEMS OF LINEAR EQUATIONS

16. a different slopes SYSTEM OF LINEAR EQUATIONS WITH EXACTLY ONE SOLUTION A system has e xactly one solution if the lines intersect. different /same intercepts CONSISTENT-INDEPENDENT SYSTEM

17. SYSTEM OF LINEAR EQUATIONS WITH NO SOLUTION INCONSISTENT SYSTEM

18. SYSTEM OF LINEAR EQUATIONS WITH INFINITELY MANY SOLUTIONS CONSISTENT-DEPENDENT SYSTEM

19. SUMMARY Intersecting lines Consistent-independent

20. Identify the type of system by comparing their slopes and intercepts.Give the number of solutions and describe their graphs. 1. y=x-1 2. 3y +x =5 3. y = -x + 2 y=2x+2 6y+2x=10 y = -x -5 Try this! xy =3 x-y=5

21. ALGEBRAIC METHODS OF SOLVING SYSTEMS OF LINEAR EQUATIONS

22. SUBSTITUTION METHOD x+y =3 x-y=5 1.Find the value of x in terms of y in equation 1 x=3-y

23. x+y=3 x-y=5 2.Substitute value of x in equation 2 From eq. 1. x=3-y x-y=5 (3-y )-y=5 3-2y=5 -2y=5-3, SUBSTITUTION METHOD -2y=2 -2 -2 y=-1

24. x+y=3 x-y=5 3 .Substitute value of y =-1 in equation 1 x=3-y , SUBSTITUTION METHOD x= 3-(-1) x=3+1 x=4

25. x+y=3 x-y=5 Therefore, the solution of the system is , SUBSTITUTION METHOD (4,-1)

26. This means that the lines intersect at point SUBSTITUTION METHOD (4,-1)

27. x+y=3 (4) +(-1) =3 4-1=3 3 = 3 If x=4 and y=-1, then Checking x+y=3 x-y=5 x-y=5 (4) -(-1) =5 4+1=5 5=5

28. ELIMINATION METHOD x+y=3 x-y=5 2x = 8 2 2 Add equation 1 and 2, eliminate y, since they have opposite signs and they add up to zero x = 4

29. x+y=3 x-y=5 Substitute value of x in either equation 1 or 2 x = 4 4+y=3 y=3-4 y=-1 ELIMINATION METHOD

30. x+y=3 x-y=5 The solution to the system is (4, -1) ELIMINATION METHOD

31. x+y=3 (4) +(-1) =3 4-1=3 3 = 3 If x=4 and y=-1, then Checking x+y=3 x-y=5 x-y=5 (4) -(-1) =3 4+1=5 5=5

32. Solve the system: y=x-1 y=2x+2 Try this! x+y=3 x-y=5

33. Solve the system of equations. 1. y=x-1 2. 3y +x =5 3. y = -x + 2 y=2x+2 6y+2x=10 y = -x -5 Try this! xy =3 x-y=5

34. Try this! x+y=3 x-y=5