1. Solving Equations Equation of degree1 Equation of degree2

2. . Introduction- Objectives Solving equations can get confusing when too many variables are floating about. But when you keep thing straight it is easy and fun Lesson Objectives: From the presented materials,at the end of the lesson, students should be able to solve any equation of fist and second. Outcomes At the end of this lesson, all students should be able to: Understand how the mechanism of equation of degree1 At the end of this lesson, all students should be able to: Understand how the mechanism of equation of degree2 At the end of this lesson, all students should be able to: Solve with confident any equations of degree 1 and 2

3. Equations of degree1 A first-degree equation is called a linear equation. The highest exponent of a linear equation is 1. The standard form for a linear equation is: ax + b = c, where a, b, and c are constants (numbers). To solve a first-degree equation, we use the following steps: If parentheses occur, multiply to remove them using the parentheses rules learned. Collect like terms. Use the addition/subtraction property to get all terms with a variable on one side and all numbers on the other side. Collect like terms. Apply the multiplication/division property to solve for the variable. Verify the solution. Remember : Equations behave like a balance. So we need to apply the same operation to both sides of an equation to maintain the balance. This means we can: add the same number to both sides of an equation subtract the same number from both sides of an equation multiply both sides of an equation by the same number divide both sides of an equation by the same number

4. Example1 4x-16=0 In solving this equation we want find the value of X that make the expression true. “X” is then called the unknown. When dealing with equations it is better to place all known value on one side of the “=” sign. But remember everything you move changes its sign. If the sign was “+” it changes to “– “and vice versa So: we can separate 4x and 16 4x=16. The sign of 16 changes from -16 to +16 Find the value of X. To find X all we have to do is divide 16 by 4. So x=4 Let’s verify: 4x4=16 The general formula of what we just did is : Ax+b=o Then X=b/a

5. 4X+8 = -12 1. X = 4 2. X = 5 3. X = -5

6. Example2

7. 5X+2 = -X+10 9/22/2015 7 1. X = 2 2. X = 4/3 3. X = -7

8. Example3

9. Y/10 = 29/22/2015 9 1. Y = 4 2. Y = 20 3. Y = -5

10. Example4 With parentheses

11. 3(2X-3)+4X =5(X+4)-9 9/22/2015 11 1. X = 4 2. X =12 3. X =1

12. Equations of degree2 First degree equations A second-degree equation is called a quadratic equation. The highest exponent of a quadratic equation is 2.The general form of these equations is ax 2 +bx +c = 0; where a, b, and c are constants and “a” is not equal 0. The solution for this type of equation can often be found by a method known as factoring, because really the second degree equation is the product of two first degree equations. so it can be factored into these equations. BUT, Finding the factors of a quadratic equation is not always easy. To solve this problem, the quadratic formula was invented so that any quadratic equation can be solved. The quadratic equation is stated as follows for the general equation ax 2 + bx + c = 0

13. Example1 9/22/2015 13

14. x 2 - x – 6 =09/22/2015 14 1. X=(1,4) 2. X=(5,8) 3. X=(-2,3)

15. Example2 9/22/2015 15

16. x 2 + 4x +4 =09/22/2015 16 1. X=(3,6) 2. X=-2 3. X=(1,0)

17. Example3 9/22/2015 17

18. x 2 - 16 =09/22/2015 18 1. X=(2,2) 2. X=(0,1) 3. X=(-4,4)

19. Example: Using factors If you can easily find the factors the composed the second degree equation you can use it instead of the quadratic formula. x 2 - 1 = 0 by factoring we get (x + 1)(x - 1) = 0 x = ±1 Or this equations x 2 - 5x + 6 = 0 (x - 2)(x - 3) = 0 x = 2, 3 9/22/2015 19

20. (X-6)(X+5)=0 9/22/2015 20 1. X=(0,0) 2. X=(6,-5) 3. X=(7,4) 10