Solve simultaneous linear equations: x – 3y = 3x – 1 = 2x – y.
Solution:
It is given that
x – 3y = 3x – 1 = 2x – y
Here
x- 3y = 3x – 1
x – 3x – 3y = – 1
By further calculation
– 2x – 3y = – 1
2x + 3y = 1 ….. (1)
3x – 1 = 2x – y
3x – 2x + y = 1
By further simplification
x + y = 1 ….. (2)
Multiply equation (2) by 2 and subtract from equation (1)
2x + 3y = 1
2x + 2y = 2
So we get
y = – 1
Substitute the value of y in equation (1)
2x + 3 (-1) = 1
So we get
2x – 3 = 1
2x = 1 + 3 = 4
By division
x = 4/2 = 2
Therefore, x = 2 and y = – 1.
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