Solve simultaneous linear equations: (i) 15x – 14y = 117

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Solve simultaneous linear equations:

(i) 15x – 14y = 117
14x – 15y = 115
(ii) 41x + 53y = 135
53x + 41y = 147.

Solution:

(i) 15x – 14y = 117 ….. (1)
14x – 15y = 115 ….. (2)
Now multiply equation (1) by 14 and (2) by 15
210x – 196y = 1638 …. (3)
210x – 225y = 1725 ….. (4)
By subtracting both the equations
29y = – 87
So we get
y = -87/29 = – 3
Substitute the value of y in equation (1)
15x – 14 (-3) = 117
By further calculation
15x + 42 = 117
So we get
15x = 117 – 42 = 75
By division
x = 75/15 = 5
Therefore, x = 5 and y = – 3.
(ii) 41x + 53y = 135 ….. (1)
53x + 41y = 147 ….. (2)
Now multiply equation (1) by 53 and (2) by 41
2173x + 2809y = 7155 ….. (3)
2173x + 1681y = 6027 ….. (4)
By subtracting both the equations
1128y = 1128
So we get
y = 1128/1128 = 1
Substitute the value of y in equation (1)
41x + 53 × 1 = 135
By further calculation
41x + 53 = 135
So we get
41x = 135 – 53 = 82
By division
x = 82/41 = 2
Therefore, x = 2 and y = 1.

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