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Linear equation

Linear equation in one variable
its more like algebraic expression What was taught in class vii in i.c.s.e board and C.B.S.E board
Some solved Examples are given in simple way
For eg:Q 1. 3x-5 = 2x+8 ( as R.H.S=L.H.S)
3x-2x=8+5(as side is changed -ve sign becomes +ve sign n +ve sign becomes -ve)
x=13
Q.2 6-3(2x-3)=5(6-x)-4x
6-6x+9=30-5x-4x(by breaking the bracket on both side)
15-6x=30-9x
9x-6x=30-15
3x=15
x=15/3
x=5
Q3.(x/7)-(x/3)=12
(3x-7x)/21= 12
(-4x)/21=12
x=(12/-4)*21
x=-63
Q.4 (3x/2)-3/2=(4x/3)-2
(3x/2)-(4x/3)=-2+3/2
(9x-8x)/6= (-4+3)/2
x/6=-1/2
x=-3
Q5. (2x+3)/(3x+4)=(2x-3)/(3x-2)
(2x +3)*(3x-2)=(2x-3)*(3x-2)
2x*(3x-2)+3*(3x-2)=2x*(3x-2)-3*(3x-2)
6x2-4x+9x-6=6x2-4x-3*(3x-2)
6x2+5x-6=6x2-4x-9x+6
5x-6=-13x+6
18x=12
x=12/18
Q6.1.25+9.75/x=4.5
(1.25x+9.75)/x=4.5
1.25x+9.75=4.5x
4.5x-1.25x=9.75
3.25x=9.75
x=(9.75)/3.25
x=975/325
x=195/65=39/13=3

Solve the following:


Q 1.4X-9=2X+7

Q 2.5y+18= 11-2y

Q 3. 3(y-7)-2(3y-4)=(2-5y)

Q 4.2x-1/3x-1=2x+3/3x+4

Q 5.3(t-5)-16t=12-2(t-3)

 Q 6.(2-9x)/(16+5x)=0

Q 7.(3/x-2)-(2/x-3)=(4/x-3)-(3/x-1)

Q 8.(z+3)(z-3)-z(z+5)=6

Q 9.(x+6/4)-(5x-4/8)+ (x-3/5)=0

Q 10.3/4(7x-1)-(2x-1-x/2)=x+3/2 
   
 WORD PROBLEM


                
 
                    1.Suresh has Rs3456.Suresh's sister has x amount of money.The total
                    amount of money is Rs.455678.Find the amount of suresh's sister money.

                   2. Sohail age is x and his son age is 3th of sohan's age,difference between
                    their ages is 44.Find their ages.

                   3. Mahesh age is 1/2 of Suresh age.After 10 years their age difference will be 4 . Find their present age.

                   4. Akash age is 1/3 of Suresh age.After five years Akash age would be 1/2 of Suresh age.Find their present age.


                   5. Rohan bought x apples and (1/3)x oranges, no of total fruits are 345.Find the no of apples,no of oranges.

                   6.Suresh bought some number of eggs,The cost of eggs are Rs.60 per dozen.He pays Rs.1120 to shopkeeper.
                    Find the number of eggs Suresh had.

                   7.Sohan has one cardboard having length 4/5 of his breadth.Perimeter of cardboard is 540cm.Find the length
                    and breadth.

                    8.Perimeter of a square box is 6400cm.Find the side of the square.

                   9.Rakesh has some  amount of money, he pays 3/5 to Prakash. Find the money Prakash got, when the 
                    left amount is Rs.56000 of Rakesh after giving Prakash.

                   10.Mohan's age is 1/2 of his father's age and their age difference is 22.Find their age.

LINEAR EQUATION IN TWO VARIABLE


Let's understand this with some basic examples given below
Q1. 3x-y=10,5x+2y=24. Ans: The given equations are: 3x-y=10....(i)
5x+2y=24.....(ii)
y=-10+3x
(from i) 5x+2(3x-10)=24
5x-20+6x=24
11x=44
x=4

 Q 2. 3x-4y=0, 6y-4x=1/6
Ans: 3x-4y=0....(i)
6y-4x=1...(ii)
3x=4y ...from (i)
x=4y/3
6y-4(4y/3)=1
6y-16y/3=1
(18y-16y)/3=1
2y/3=1
y=3/2
Q3.8/x-5/y=34,3/x-2/y=13
Ans: 8/x-5/y=34...(i)
by multiplying (i) with 3 and (ii) with 8
3/x-2/y=13...(ii)
we get (i)
(24/x)-(15/y)=34*3
we get (ii)
(24/x)-(16/y)=13*8
by substracting (ii) from (i)
( 16/y)-(15/y)=34*3-13*8
(16y-15y)/y=102-104
1/y=-2

1=-2y
1/-2=y

y=-1/2
1/y= -2,by putting it in(i)
(8/x-5/2=34
8/x=34-5/2=63/2
x/8=2/73 x=16/73 		Q.4: (3.4/x)+3=(4.5/y)-4
(2.2/x)+2=-(6/y)-4
(3.4)/x-(4.5)/y=-7-(i)
(2.2/x)+6/y=-6-(ii)
by multiplying (i) with 6 we get( 20.4/x)-(27/y)=-42-(i)
by multiplying (ii) with 4.5 we get(9.9/x)+(27/y)=-27-(ii)
by adding (i) with (ii)
(20.4/x)-(9.9/x)=42-27
10.5/x=15
1/x=150/105
1/x=10/7
by putting it in(eq ii)we get
99/7+27/y=-27
27/y=-27
27/y=-((27*7)-99)/7
27/y=
SOLVE THE PROBLEM
1)2x-y=3,3x+y=6

2)3x+y=4,5x-2y=5

3)4x+y=5,y=6x+15

4)5x-5=y,8y=3.5x+5

5)(5/x)+(6/y)=(2/x)-(5/y)+3,(3/x)+(2/y)=3

 6) (x+4)/(y-5)=5/6,(x-4)/(y-4)=7/8

7)(4.5x+5)/(6.5y-5)=3/5,(4x-6)/(6.5y-3)=8/9

8)(6/7x)+(9/3y)=3/5,(2/2x)+(9/3y)=9/8

9)(x+y)/3(x-y)=2/3,3(x+y+1)/3(x-y)=9/8

10)(4x/4y)+1=4,3(x+y)=1 

 
 WORD PROBLEM FOR LINEAR EQUATION IN TWO VARIABLE
   
            
  Q1.The sum of two integers is 60 and the difference is 6.Find the numbers .
 
              Q2. If 3 is substracted from numerator and denomenator, then the fraction becomes 4/5,if 1 is added the fraction becomes 2/3.

              Q3 .A two digit number is 5 times the sum of its digits.If 9 is added to the number ,its digits are reversed.Find the number.

              Q4. The weekly incomes of A and B are in the ratio 5:6 and their weekly expenditure are in the ratio 8:11.If each saves Rs.1050 per week, find their weekly income.

              Q5. 6 nuts and 5 bolts weigh 300 gm while 8 nuts and 1 bolt weigh 278 gm.Find the weigh of 1 nut and 1 bolt.

              Q6. A boat can go 75km downstream  in 5 hrs and 44km in upstream in 4 hrs.Find the speed of the boat in still water and speed of the current.

              Q7 .On adding 1 to the numerator of the fraction,it becomes 1/2 while adding 1 to the denomenator it becomes 1/3.Find the fraction.

              Q8. Six years ago,the ages of geeta and seema were in ratio 3:4.Nine years hence their ages will be in the ratio 6:7.Find their ages.

              Q9. The sum of two numbers is 30 and the difference of their squares is 180.Find the numbers.

              Q10. Twice of a number is equal to thrice of the number.If the sum of the numbers is 85.Find the numbers.