Solve the following systems of simultaneous linear equations by cross-multiplication method:
(i) 3x + 2y = 4
8x + 5y = 9
(ii) 3x – 7y + 10 = 0
y – 2x = 3.
Solution:
(i) 3x + 2y = 4
8x + 5y = 9
We can write it as
3x + 2y – 4 = 0
8x + 4y – 9 = 0
By cross multiplication method
x/ (-18 + 20) = y/ (-32 + 27) = 1/ (15 – 16)
By further calculation
x/2 = y/-5 = 1/-1
So we get
x/2 = – 1
x = – 2
y = – 5 (-1) = 5
Therefore, x = – 2 and y = 5.
(ii) 3x – 7y + 10 = 0
y – 2x = 3
We can write it as
3x – 7y + 10 = 0
y – 2x – 3 = 0
By cross multiplication method
x/ (21 – 10) = y/ (-20 + 9) = 1/ (3 – 14)
By further calculation
x/11 = y/-11 = 1/-11
So we get
x/11 = 1/-11
x = – 1
Similarly
y/-11 = 1/ -11
y = 1
Therefore, x = – 1 and y = 1.
More Solutions:
- Solve simultaneous linear equations: (i) 2a(2)x – bx + 2a(2) – b
- Solve simultaneous linear equations: (i) (x2 – y2)z + (y2 – z2)x
- Solve simultaneous linear equations: (i) b(c -d)2 + a(d – c) + 3c – 3d
- Solve simultaneous linear equations: (i) x(x + z) – y (y + z)
- Solve simultaneous linear equations: (i) 9×2 + 12x + 4 – 16y2
- Solve simultaneous linear equations: (i) 21×2 – 59xy + 40y2
- Solve simultaneous linear equations: (i) x2y2 – xy – 72
- Solve simultaneous linear equations: (i) (3a – 2b)2 + 3(3a – 2b) – 10
- Solve simultaneous linear equations: (i) (x2 – x) (4×2 – 4x – 5) – 6