Presentation is about linear equations.pptx

presentation is about linear equations .

1. Today’s Goal ! Meaning of the Chapter’ Solution of an Equation. Word problems. ( Applications of linear equation in one variable.)

2. Terms Constants & Variables Algebraic Expression Equation

3. EQUATION    ​ A statement which states that two algebraic expressions are equal is called an equation. ​ 3x-2y=8 6-x = x+9 LINEAR EQUATION IN ONE VARIABLE ​ ​ The equation involving only one variable in first order is called a linear equation in one variable ​ 3x-5=0 8-y=2

4. Linear Equation in one variable. Equation 2x -3 =7 Variables Equality

5. Solve an Equation ​ 1.To solve an equation of the form  x+a =b ​ Eg : Solve x+6=10​ Sol: x+6=10            => x+6-6=10-6   {subtracting 6 from both sides}​                                    =>  x=4 ​ 2.  To solve an equation of form x-a=b​ Eg : Solve y-4=6​ Sol: y-4=6          = > y-4+4=6+4   {adding 4 on both sides}​                             => y=10​

6. Transpose the terms containing the variables to one side and constants to the other side ​ ​ EXAMPLE 1     Solve 10y-3=7y+9 ​    SOL:         10y-7y=9+3    (transposing 7y to left & 3 to the right) ​                    => 3y=12 ​                    => y=12/3 ​                    => y = 4 ​ EXAMPLE 2     Solve 2(x-5) + 3(x-2) = 8+7(x-4) ​    SOL:           2x-10+3x-6 = 8=7x-28  (removing the brackets) ​                     => 5x-16 = 7x-20 ​                     => 5x-7x = -20+16 ​                     => -2x = -4 ​                     => x = -4/-2 ​                    => x = 2 ​ SOLVING EQUATIONS WITH VARIABLE ON BOTH SIDES ​

7. SOLVING WORD PROBLEMS ​  QUES : A number increased by 8 equal 15. Find the number ? ​ Solution: Let the number be 'x' ​ => x+8 = 15 ​ => x = 15-8 ​ => x = 7 ​

8. QUES:    A number is decreased by 15 and the new number so obtained is multiplied by 3; the result is 81. Find the number ? ​ SOLUTION:         Let the number be 'x' ​                             The number decreased by 15 = x-15 ​                             The new number (x-15) multiplied by 3 = 3(x-15) ​                 Given 3(x-15) = 81 ​                            => 3x-45=81 ​                            => 3x=81+45 ​                            => x=126/3 ​                            => x=42           

9. QUES :  A man is 26 years older than his son. After 10 years, he will be three times as old as his son. Find their present ages. ​ SOL:    Let son's present age= x years ​            Then father's age = x+26 years ​             After ten years, ​                  Son's age = x+10 ​                  Father's age = x+26+10 = x+36 ​    Given,      x+36=3(x+10) ​                      => x+36 = 3x+30 ​                      => x-3x = 30-36 ​                      => -2x = -6 ​                      => x = -6/-2 ​                      => x = 3 ​ Son's age = 3 years ​ Father's age = 3 + 26 = 29 years ​