Solve simultaneous linear equations:
(i) 3/x + 4y = 7
5/x + 6y = 13
(ii) 5x – 9 = 1/y
x + 1/y = 3.
Solution:
(i) 3/x + 4y = 7 ….. (1)
5/x + 6y = 13 ….. (2)
Substitute 1/x = a in equation (1) and )@)
3a + 4y = 7 …. (3)
5a + 6y = 13 ….. (4)
Multiply equation (3) by 5 and (4) by 3
15a + 20y = 35
15a + 18y = 39
Subtracting both the equations
2y = -4
So we get
y = – 4/2 = – 2
Substitute the value of y in equation (3)
3a + 4 (-2) = 7
By further calculation
3a – 8 = 7
3a = 7 + 8 = 15
So we get
3a = 15
a = 15/3 = 5
Here x = 1/a = 1/5
Therefore, x = 1/5 and y = – 2.
(ii) 5x – 9 = 1/y ….. (1)
x + 1/y = 3 ….. (2)
Substitute 1/y = b in (1) and (2)
5x – 9 = b
5x – b = 9 ….. (3)
x + b = 3 ….. (4)
By adding equation (3) and (4)
5x – b = 9 ….. (3)
x + b = 3 ….. (4)
So we get
6x = 12
By division
x = 12/6 = 2
Substitute the value of x in equation (4)
2 + b = 3
b = 3 – 2
b = 1
Here 1/y = 1
b = 1/y
y = 1
Therefore, x = 2 and y = 1.
More Solutions:
- Solve the linear equations (i) x + y = 14:
- Solve the linear equations (i) a + 3b = 5:
- Solve the linear equations: (i) 2x – 3y/4 = 3
- Solve the linear equations: (i) mx – ny = m2 + n2
- Solve 2x + y = 35, 3x + 4y = 65.
- Solve the simultaneous equations 3x – y = 5, 4x – 3y = – 1.
- Solve simultaneous linear equations: (i) 3x + 4y = 10
- Solve simultaneous linear equations: (i) ¾ x – 2/3 y = 1
- Solve simultaneous linear equations: (i) 15x – 14y = 117