Can the following equations hold simultaneously?

by

Can the following equations hold simultaneously?

3x – 7y = 7
11x + 5y = 87
5x + 4y = 43.
If so, find x and y.

Solution:

3x – 7y = 7 …… (1)
11x + 5y = 87 ….. (2)
5x + 4y = 43 ….. (3)
Now multiply equation (1) by 5 and (2) by 7
15x – 35y = 35
77x + 35y = 609
By adding both the equations
92x = 644
By division
x = 644/92 = 7
Substitute the value of x in equation (1)
3 × 7 – 7y = 7
By further calculation
21 – 7y = 7
So we get
– 7y = 7 – 21 = – 14
y = – 14/ – 7 = 2
Therefore, x = 7 and y = 2.
If x = 7 and y – 2 satisfy the equation (3) then we can say that the equations hold simultaneously
Substitute the value of x and y in equation (3)
5x + 4y = 43
By further calculation
5 × 7 + 4 × 2 = 43
So we get
35 + 8 = 43
43 = 43 which is true.
Therefore, the equations hold simultaneously.

More Solutions:

Leave a Comment