10th CBSE maths solution for exercise 3.3 part 3

This page 10th CBSE maths solution for exercise 3.3 part 3 is going to provide you solution for every problems that you find in the exercise no 3.3

10th CBSE maths solution for Exercise 3.3 part 3

(2) Solve 2 x  + 3 y = 11 and 2 x - 4 y = -24 and hence find the value of "m" for which y = m x + 3

Solution:

   2 x  + 3 y = 11 ----------- (1)

   2 x - 4 y = -24 ----------- (2)

Step 1: Find the value of one variable in terms of other variable

   3 y = 11 - 2 x

     y = (11 - 2 x)/3

now we are going to apply the value of y in terms of x in the other equation

       2 x - 4 (11 - 2 x)/3 = -24

       14 x - 44 = -24 (3)

       14 x - 44 = -72

         14 x = - 72 + 44

         14 x = - 28

              x = -28/14

              x = -2

Substitute x = -2  in the equation y = (11 - 2 x)/3

                         y = [11 - 2(-2)]/3   

                         y = (11 + 4)/3

                         y = 15/3

                          y = 5

now we have to apply these values in the equation y = m x + 3 in-order to get the value of m

  5 = m (-2) + 3

  5 = -2 m + 3

  5 -3 = - 2 m

   -2 m = 2

        m = 2/(-2)

        m = -1


(3) Form the pair of linear equations of the following problems and find their solution by substitution method.

(i) The difference between two numbers is 26 and one number is three times the other. Find them

Solution:

Let the two numbers are "x" and "y"

Difference between two number is 26

x - y = 26 -------- (1)

One number is three times the other

x = 3 y -------- (2)

now we are going to apply the value of x in the first equation

3 y - y = 26

 2 y = 26

    y = 26/2

    y = 13

now, we have to apply the value of y in the second equation

   x = 3 (13)

   x = 39

Therefore the required two numbers are 39 and 13.


(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them

Solution:

Let the two supplementary angles are "x" and "y"

so, sum of these two angles is 180

 x + y = 180 -----(1)

the larger angle exceeds the smaller by 18

 x = y + 18 -----(2)

Now,we are going to apply the value of x in the first equation

y + 18 + y = 180

   2 y = 180 - 18

   2 y = 162

     y = 162/2

     y = 81

 x = 81 + 18

 x = 99

Therefore the two supplementary angles are 99 and 81.




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