Solve the linear equations (i) x + y = 14:

by

Solve the linear equations:

(i) x + y = 14
x – y = 4
(ii) s – t = 3
s/3 + t/2 = 6
(iii) 2x + 3y = 9
3x + 4y = 5
(iv) 3x – 5y = 4
9x – 2y = 7

Solution:

(i) x + y = 14
x – y = 4
It can be written as
x = 4 + y
By substituting the value in the above equation
4 + y + y = 14
By further calculation
2y = 14 – 4 = 10
Dividing by 2
y = 10/2 = 5
So we get
x = 4 + 5 = 9
Hence, x = 9 and y = 5.
(ii) s – t = 3
s/3 + t/2 = 6
By taking LCM
2s + 3t = 6 × 6 = 36
We know that
s – t = 3 …. (1)
2s + 3t = 36 ….. (2)
So we get
s = 3 + t …. (3)
By substituting the value of s in equation (2)
2 (3 + t) + 3t = 36
By further calculation
6 + 2t + 3t = 36
So we get
5t = 36 – 6 = 30
By division
t = 30/5 = 6
Substituting t in equation (3)
s = 3 + 6 = 9
Hence, s = 9 and t = 6.
(iii) 2x + 3y = 9 …. (1)
3x + 4y = 5 ….. (2)
Equation (1) can be written as
2x = 9 – 3y
x = (9 – 3y)/ 2 …. (3)
By substituting the value of x in equation (2)
3 × (9 – 3y)/ 2 + 4y = 5
By further calculation
(27 – 9y)/ 2 + 4y = 5
By taking LCM
27 – 9y + 8y = 10
So we get
-y = – 17
y = 17
Substituting y in equation (3)
x = [9 – (3 × 17)]/ 2
By further calculation
x = (9 – 51)/ 2
x = – 21
Hence, x = – 21 and y = 17.
(iv) 3x – 5y = 4 ….. (1)
9x – 2y = 7 …. (2)
Multiply equation (1) by 3
9x – 15y = 12
9x – 2y = 7
By subtracting both the equations
– 13y = 5
y = -5/13
Equation (1) can be written as
3x – 5y = 4
x = (4 + 5y)/ 3 ….. (3)
By substituting the value of x in equation (2)
9 [(4 + 5y)/ 3] – 2y = 7
By further calculation
12 + 15y – 2y = 7
13y = – 5
So we get
y = -5/13
Substituting y in equation (3)
Simultaneous Linear Equations Class 9 ICSE ML Aggarwal img 1
Hence, x = 9/13 and y = – 5/13.

More Solutions:

Leave a Comment