solve using elimination method

 solve using elimination method

 

10x +5y =110

5x+8y   =88 

first decide which unknow you are going to eliminate

If we decide to eliminate x

make the coefficient of x same

so multiply the second equation with 2

then subtract to eliminate x and solve for y

resubstitute in any one of the equations for x.

10x +5y =110

[5x+8y   =88 ]*2

 

 10x +5y   =110

10x + 16y =176 

------------------------------subtracting

      (-11)y =(-66)

          y = (-66)/(-11)

         y =6

resubstitute in 5x+8y   =88

5x +48 =88

5x=88-48

5x=40

x=8 

2. Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs.27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day. 

solution

(iv) Meena went to a bank to withdraw Rs.2000. She asked the cashier to give her
Rs. 50 and Rs.100 notes only. Meena got 25 notes in all. Find how many notes of
Rs.50 and Rs.100 she received.

solution

 

(iii) 

(iii)The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number 

solution

 (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

solution

 

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes (1/2) if we only add 1 to the denominator. What is the fraction?

solution  

 

Solve the following pair of linear equations by the elimination method and the substitution method : 

 x + y = 5 and 2x – 3y = 4

solution  

(ii) 3x + 4y = 10 and 2x – 2y = 2 

 

solution

 (iii) 3x – 5y – 4 = 0 and 9x = 2y + 7

  solution

 

 

iv)

(x/2)+(2y/3)=(-1)

 x -(y/3)=3

solution

 

exercise 3.3

solve by method of substitution 

(ii) 

s-t =3

(s/3)+(t/2)=6

solution

(iii)

 3x – y = 3

9x – 3y = 9

solution  

(iv) 

0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3 

solution

(v)

 sqrt(2)x +sqrt(3)y =0

sqrt(3)x -sqrt(8)y =0

solution

 

(vi)

(3x/2)-(5y/3)=(-2)

(x/3)+(y/2)=(13/6)

solution

 

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

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

solution

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

solution 

(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, she buys 3 bats and 5 balls for Rs.1750. Find the cost of each bat and each ball.

 solution 

 

(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs.155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

solution

v) A fraction becomes (9/11) if 2 is added to both the numerator and the denominator.  If 3 is added to both the numerator and the denominator it becomes (5/6). Find the fraction.

solution  

 

(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

solution

 

exercise 3.2

form the equations and solve by graphical method

  10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

solution

5.

 Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

 solution

 

 
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