Question 1. Solve the Following Pair of Linear Equations By the S Exercise 3.3 Chapter 3 Pair of Linear Equations in

Question 1. Solve the following pair of linear equations by the substitution method.
(i) x + y = 14  ; x – y = 4                                (ii) s – t = 3 ; s/3 + t/2 = 6
(iii) 3x – y = 3 ; 9x – 3y = 9                          (iv) 0.2x + 0.3y = 1.3  ; 0.4x + 0.5y = 2.3
(v)√2 x+  √3y =  0 ; √3 x -  √8y =  0 (vi)3/2 x -  5/3y = -2 ; x/3 +  y/2 = 13/6

Solution: (i) x + y = 14  ; x – y = 4 

solve first equation
x + y    = 14
x          = 14 - y  …………..(1)
plug this value in equation second we get
x – y    = 4
14 – y   - y      = 4
Add 14 both side we get
- 2 y     = 4 - 14
- 2 y     = - 10
Y         = -10/-2
Y         = 5
Plug y = 5 in equation first we get
X         = 14 – y
X         = 14 – 5
X         = 9
Answer x  = 9 , y = 5

(ii)s – t = 3 ; s/3 + t/2 = 6

Solve first equation
s – t     = 3 
s          = 3+t …………(1)
Plug this value in equation second we get
s/3 + t/2          = 6

Multiply by 6 to remove all denominator we get
6 + 2t  +  3t     =  36
5t         = 36 – 6
5t         = 30
Divide by 2 we get
t           = 30/5
t           =6
Plug the value in equation first we get
s          = 3 +6
s          = 9
Answer s  = 9 , t = 6

(iii)3x – y = 3 ; 9x – 3y = 9     

solve first equation
3x – y = 3
3x        =3 +y
x         = (3 + y)/3  …………..(1)
Plug this value in equation second we get

9 is always equal to 9
So it is a true condition and in such condition
Equations will have many or infinity solutions

(iv) 0.2x + 0.3y = 1.3      …..(1)  ;

0.4x + 0.5y = 2.3                               ...(2)
0.2x + 0.3y = 1.3 
Solve first equation we get
0.2x  = 1.3 – 0.3y
Divide by 0.2 we get
X        = 1.3/0.2   - 0.3/0.2
X         = 6.5 – 1.5 y              …(3)
Plug the value in equation second we get
0.4x + 0.5y   = 2.3
(6.5 – 1.5y)*0.4x + 0.5y        =  2.3
2.6 – 0.6y + 0.5y       = 2.3
-0.1 y  = 2.3 – 2.6
Y         = - 0.3/-0.1
Y         = 3
Plug this value in equation 3 we get 
X         = 6.5 – 1.5 y
X         = 6.5 – 1.5(3)
X         =6.5  - 4.5
X         =2
Answer x = 2, y = 3

(v)√2 x+  √3y =  0                            ...(1)

√3 x -  √8y  = 0                              ... (2)  
√2 x+  √3y =  0
Subtract √3y both side we get
√2 x     =  -√3y
Divide by √2

Plug the value of x in equation first we get
√3 x -  √8y =  0

Plug this value in equation (3) we get

Our answer   x = 0 and y = 0

(vi) 3/2 x -  5/3y = -2                                                       ……(1)

 x/3 +  y/2 = 13/6                                                       .......(2)
Solve first equation
3/2 x -  5/3y    = -2
Multiply by 6 to remove all denominator we get
9 x – 10 y       = -12
9x      = -12 + 10y
Divide by 9 we get
x          = (-12 + 10 y)/9                      …..(3)
plug this value in equation (2) we get

Multiply by LCM of denominator  = 27* 2  = 54 we get
2(-12 +10 y ) +  27 y= 117
-24 +  20 y + 27 y      = 117
47 y     = 117  +  24
Y        = 141/47         = 3
Plug this value in equation (3) we get
x          = (-12 + 10*3)/9
x=18/9
x          = 2
Answer x = 2 and y = 3