Solve the simultaneous equations 3x – y = 5, 4x – 3y = – 1. Hence, find p, if y = px – 3.
Solution:
It is given that
3x – y = 5 ….. (1)
4x – 3y = – 1 ….. (2)
Now multiply equation (1) by 3
9x – 3y = 15 ….. (3)
4x – 3y = – 1 ….. (4)
Subtracting equation (3) and (4)
5x = 16
x = 16/5
Substitute the value of x in equation (3)
3 × 16/5 – y = 5
By further calculation
48/5 – y = 5
48/5 – 5 = y
Taking LCM
(48 – 25)/ 5 = y
So we get
y = 23/5
We know that
y = px – 3
23/5 = p × 16/5 – 3
Substitute the value of x and y
23/5 + 3 = 16p/5
Taking LCM
(23 + 15)/ 5 = 16p/5
By further calculation
38/5 = 16p/5
So we get
16p = 38
p = 19/8
Therefore, x = 16/5, y = 23/5 and p = 19/8.
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