Solve simultaneous linear equations: (i) x/6 = y – 6

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Solve simultaneous linear equations:

(i) x/6 = y – 6
3x/4 = 1 + y
(ii) x – 2/3 y = 8/3
2x/5 – y = 7/5.

Solution:

(i) x/6 = y – 6
3x/4 = 1 + y
We can write it as
x = 6 (y – 6)
x = 6y – 36
x – 6y = – 36 ….. (1)
3x/4 = 1 + y
By cross multiplication
3x = 4 (1 + y)
So we get
3x = 4 + 4y
3x – 4y = 4 …. (2)
Multiply equation (1) by 3
3x – 18y = – 108
3x – 4y = 4
Subtracting both the equations
– 14y = – 112
So we get
y = – 112/- 14 = 8
Substitute the value of y in equation (1)
x – 6 × 8 = – 36
By further calculation
x – 48 = – 36
x = – 36 + 48
x = 12
Therefore, x = 12 and y = 8.
(ii) x – 2/3 y = 8/3
2x/5 – y = 7/5
We can write it as
x – 2/3 y = 8/3
Taking LCM
(3x – 2y)/ 3 = 8/3
By cross multiplication
3x – 2y = 8/3 × 3 = 8
3x – 2y = 8 ….. (1)
2x/5 – y = 7/5
Taking LCM
(2x – 5y)/ 5 = 7/5
By cross multiplication
2x – 5y = 7/5 × 5 = 7
2x – 5y = 7 …… (2)
Multiply equation (1) by 2 and (2) by 3
6x – 4y = 16 ….. (3)
6x – 15y = 21 …… (4)
Subtracting both the equations
11y = – 5
y = – 5/11
Substitute the value of y in equation (1)
3x – 2 (-5/11) = 8
By further calculation
3x + 10/11 = 8
We can write it as
3x = 8 – 10/11
Taking LCM
3x = (88 – 10)/ 11 = 78/11
By cross multiplication
x = 78/ (11 × 3) = 26/11
Therefore, x = 26/11 and y = – 5/11.

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