RD Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3 Solutions
Question - 41 : - 
Answer - 41 : -
Question - 42 : - 
Answer - 42 : -
Question - 43 : - 152x – 378y = -74
– 378x + 152y = -604
Answer - 43 : -
152x – 378y = -74 ……..(i)
– 378x + 152y = -604 ………(ii)
Adding (i) and (ii), we get
– 226x – 226y = 678
Dividing by -226,
x + y = 3 ……..(iiii)
and subtracting (ii) from (i)
530x – 530y = 530
Dividing by 530,
x – y = 1 ……..(iv)
Adding (iii) and (iv)
2x = 4
x = 2
From (iii), 2 + y = 3
y = 3 – 2 = 1
Hence x = 2, y = 1
Question - 44 : - 99x + 101y = 499
101x + 99y = 501
Answer - 44 : -
99x + 101 y = 499 ….(i)
101x + 99y = 501 ……(ii)
Adding we get
200x + 200y = 1000
x + y = 5 ……(iii)
(Dividing by 200)
Subtracting we get
-2x + 2y = -2
=> x – y = 1 ….(iv)
(Dividing by -2)
Now adding (iii) and (iv)
2x = 6 => x = 3
and subtracting (iv) from (iii)
2y = 4 => y = 2
Hence x = 3, y = 2
Question - 45 : - 23x – 29y = 98
29x – 23y = 110
Answer - 45 : -
23x – 29y = 98 ….(i)
29x – 23y = 110 ….(ii)
Adding (i) and (ii) we get
52x – 52y = 208
x – y = 4 ….(iii)
(Dividing by 52)
Subtracting (ii) from (i)
6x + 6y = 12
=> x + y = 2 ….(iv)
(Dividing by 6)
Adding (iii) and (iv)
2x = 6 => x = 3
Subtracting (iv) from (iii)
2y = -2 => y = -1
Hence x = 3, y = -1
Question - 46 : - x – y + z = 4
x – 2y – 2z = 9
2x + y + 3z = 1
Answer - 46 : -
x – y + z = 4 ……(i)
x – 2y – 2z = 9 ……(ii)
2x + y + 3z = 1 ……(iii)
Question - 47 : - x – y + z = 4
x + y + z = 2
2x + y – 3z = 0
Answer - 47 : -
x – y + z = 4 ….(i)
x + y + z = 2 ….(ii)
2x + y – 3z = 0 ….(iii)
From (i)
z = 4 – x + y
Substituting the values of z in (ii) and (iii)
x + y + 4 – x + y = 2
2y = 2 – 4 = -2
y = -1
and 2x + y – 3(4 – x + y) = O
2x + y – 12 + 3x – 3y = 0
5x – 2y = 12
5x – 2(-1) = 12
5x + 2 = 12
5x = 12 – 2 = 10
x = 2
From (i),
2 – (-1) + z = 4
2 + 1 + z = 4
3 + z = 4
z = 4 – 3 = 1
Hence x = 2, y = 1, z = 1
Question - 48 : - 21x + 47y = 110
47x + 21y = 162
Answer - 48 : -
We have,
21x + 47y = 110 …(i)
47x + 21y = 162 …(ii)
Multiplying equation (i) by 47 and Equation (ii) by 21, we get
987x + 2209y = 5170 …(iii)
987x + 441y = 3402 …(iv)
Subtracting equation (iv) from equation (iii),
we get
1768y = 1768
y = 1
Substituting value of y in equation (i), we get
21x + 47 = 110
or 21x = 63
or x = 3
So, x = 3, y = 1
Question - 49 : - If x + 1 is a factor of 2x3 + ax2 + 2bx + 1, then find the values of a and b given that 2a – 3b = 4
Answer - 49 : -
Question - 50 : - 
Answer - 50 : -