Solve simultaneous linear equations:
(i) 3x + 4y = 10
2x – 2y = 2
(ii) 2x = 5y + 4
3x – 2y + 16 = 0
Solution:
(i) 3x + 4y = 10 ….. (1)
2x – 2y = 2 ….. (2)
Multiplying equation (1) by 1 and (2) by 2
3x + 4y = 10
4x – 4y = 4
By adding both the equations
7x = 14
By division
x = 14/7 = 2
Substituting the value of x in equation (2)
2 × 2 – 2y = 2
By further calculation
4 – 2y = 2
So we get
2y = 4 – 2 = 2
y = 2/2 = 1
Therefore, x = 2 and y = 1.
(ii) 2x = 5y + 4
3x – 2y + 16 = 0
We can write it as
2x – 5y = 4 …. (1)
3x – 2y = – 16 ….. (2)
Now multiply equation (1) by 3 and (2) by 2
6x – 15y = 12 ….. (3)
6x – 4y = – 32 ….. (4)
By subtracting both the equations
– 11y = 44
y = -44/11 = – 4
Substitute the value of y in equation (1)
2x – 5 (-4) = 4
By further calculation
2x + 20 = 4
So we get
2x = 4 – 20 = – 16
x = – 16/2 = – 8
Therefore, x = – 8 and y = – 4.
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