Linear Equation in 2 Variables
Ax + By = C or Ax - By = C
Where A, B and C are Constants
x & y are Variables.
Example 1 : 3x + 2y = 4 and 8x + 5y = 9 Find the Value of x & y.
Solution : We have to do same Constant for any one variable,
So, [ 3x+2y=4 ] multiply this equation with 5 ---------- 15x+10y=20,
[8x+5y=9 ] multiply this equation with 2 --------- 16x+10y=18,
Solve both equation:
15x+10y=20
- 16x+10y=18
x = -2
so we get x = -2 ,we put the value of x in this " 3x+2y=4 " equation.
3x+2y=4
3(-2)+2y=4
2y=4+6
2y=10
y=5
Here x=-2 and y=5.
Example 2 : The total cost of 6 books and 4 pencils is 34 Rs. & that of 5 books & 5 pencils is 30 Rs.Find the cost of each book & pencil Respectively.
Solution : Price of book = x & Pencil = y
Here, 6 books and 4 pencils = 6x+4y=34
5 books and 5 pencils = 5x+5y=30
Solve these 2 equations
6x+4y=34 multiply this equation with 5 ---------- 30x+20y=170,
5x+5y=30 multiply this equation with 6 ---------- 20x+20y=120,
30x+20y=170
- 20x+20y=120
10x = 50
x = 5
so we get x = 5 ,we put the value of x in this " 6x+4y=34 " equation.
6x+4y=34
6(5)+4y=34
4y=34-30
4y=4
y=1
So, cost of each book=x=5 & cost of each pencil=y=1
Example 3 : A man has some hens & cows. If the Number of heads be 48 & Number of feets is 140. Find the Number of hens.
Solution : Hen = x & Cow = y
Feet of hen = 2x, Feet of Cow = 4y. So, Number of Feet be 140 = 2x+4y
Head of hen = x, Head of Cow = y So, Number of heads be 48 = x+y
Solve both equations,
2x+4y=140
x+y=48 multiply this equation with 2 -------- 2x+2y=96,
2x+4y=140
- 2x+2y =96
2y = 44
y = 22
Put y=22 in x+y=48
x=48-22
x=26
So Number of hens = 26
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