Solve the linear equations: (i) 2x – 3y/4 = 3

by

Solve the linear equations:

(i) 2x – 3y/4 = 3
5x – 2y – 7 = 0
(ii) 2x + 3y = 23
5x – 20 = 8y

Solution:

(i) 2x – 3y/4 = 3
5x – 2y – 7 = 0
We can write it as
2x/1 – 3y/4 = 3
By taking LCM
(8x – 3y)/ 4 = 3
By cross multiplication
8x – 3y = 12 ….. (1)
5x – 2y = 7 …. (2)
Now multiply equation (1) by 2 and (2) by 3
16x – 6y = 24
15x – 6y = 21
By subtracting both the equations
x = 3
Now substituting the value of x in equation (1)
8 × 3 – 3y = 12
By further calculation
24 – 3y = 12
– 3y = 12 – 24
So we get
– 3y = – 12
y = – 12/-3 = 4
Therefore, x = 3 and y = 4.
(ii) 2x + 3y = 23
5x – 20 = 8y
We can write it as
2x + 3y = 23 …. (1)
5x – 8y = 20 …. (2)
By multiplying equation (1) by 5 and equation (2) by 2
10x + 15y = 115
10x – 16y = 40
By subtracting both the equations
31y = 75
So we get
y = 75/31 = 2 13/31
By substituting the value of y in equation (1)
2x + 3 (75/31) = 23
By further calculation
2x + 225/31 = 23
We can write it as
2x = 23/1 – 225/31
Taking LCM
2x = (713 – 225)/ 31 = 488/31
So we get
x = 488/ (31 × 2) = 244/ 31 = 7 27/31
Therefore, x = 7 27/31 and y = 2 13/31.

More Solutions:

Leave a Comment