Mathematics For 10th Class

What we are going to study :- 

Methods of solving linear equations in two variables ---

• 1.Graphical Method              2. Cramers Rule

Staying safe at home we can study math as like as in class room. In class room your teacher teach you same things that I have written you might feel that you are in class room but except teachers voice its your own voice because now it's your tern just read the given concept thoroughly  and comment me you got it or not.

To start study for any topic it is always better to brush up your previous knowledge. as you know

 'No building can stand without base'.

What we know lets recall : -  😇

          Linear Equation : An equation which contain two variables and the degree of each term     containing variables is one is called as a Linear Equation in two variables.

 In 9th std we have studied linear equation of two variables,how the equation is formed,how to             find the solution of single equation i.e. 

          if    x + y = 14.    value of   x  and   y can be 

1. x  =  9  ,  y  =  5.
2. x  =  7  ,  y  =  7.
3. x  =  8  ,  y  =  6.

x  = 10 ,  y  =  4...........Number of pairs we can get easily.

    But if  we are  considering two equations in two variables at same time for finding value of   X and Y then those two equations are called as __??

          " Simultaneous Equations"
       General form of  a linear equation is ax+by+c=0  where a,b,c are real numbers.

              

          ax + by + c = 0   

          ↓    ↓     ↓                 

          4x + 5y + 7 =0

         where a=4,             b=5,                   c=7

           Compare the given equations with general form and complete the table given below.

           

      In 9th std. some basic methods was there to solve simultaneous equations.

1)Elimination Method

           In this method we eliminate one of variables  to obtain equation in one variable and substitute value of one variable in any one of given equation and get another variable.

  for example: X+Y=14 →eq.1

                                               X-Y=2    →eq.2
        by Adding both.equation 1 and 2 we get

                         X+Y=14

                         X-Y=2

                         ━━━━

                           2X=16

∴    X=8   put X in eq.no. 1
  ∴ X+Y=14

      8+Y=14

     Y=6.
Let's complete the given activity.

2) Substitution  Method

         In this method we can express one variable in terms of  other form of one of the equations  then substituting it in the other equation we can eliminate the variable. 😐

have you got it! ohhh don't worry it is so simple..
 for example:
                       8X+3Y= 11━━━eq.1
                       3X-Y=2━━━━eq.
 In equation 2 it is easy to express Y in terms of X.
                   ∴    3X-Y=2
                   ∴ 3X-2= Y

   substitute Y= 3X-2 in equation 1
   
                         8X+3Y=11
                      ∴ 8X+3(3X-2)=11
                          8X+9X-6=11
                           17X-6=11
                         ∴17X=17
                                  X=1
           put X=1  in  Y=3X-2

           ∴Y=3(1)-2=3-2=1

           we got (X,Y)= (1,1)

 I)Graphical Method:

    In 9th std we have studied the graph of one linear equation is a straight line.

 Do You Remember?? 😊

 lets draw graph of given equation and send me 

             

                  2x-y = 2

    ►   some steps to follow for drawing a graph of  a  linear equation in two variables.

               

     1) Make a box and find at least 4 ordered pairs for given equation.(put the vale of one and get

         other by solving equation)

     2)Draw X-axis and Y-axis on the graph paper and plot the points

             

     3) see that all four points lie on same line.

              

     4) Draw a line passing through points which lie on same line.

     Now while solving simultaneous equation by graphical method draw lines of  both of given            equation  by following the above  given  equation.

    After drawing the lines check at which point both lines are touching to each other.

     "'The point at which both the lines are touching to each other will be solution of given           simultaneous equation."
   Study the given example of simultaneous equation by graphical method.

                                   
Find the solution of  given simultaneous equations  by graphical method.
1) X+Y=0   ;   2X-Y=9
2)2X-3Y=4;    3Y-X=4
3)X+Y=  5   ;  X-Y=3


DETERMINANT:
   The determinant can be viewed as a function  whose input is a square matrix and output is a number.

To study determinant and all remaining chapters of algebra in detail with solution of all the questions of exercise just follow the blog and reply me in comment section.