Soustava rovnic
1) Vypočítejte soustavy rovnic o dvou neznámých:
x – 2y = 4
x + 3y = 6
3x + 2y = 6
4x + y = 8
– 4x + 5y = – 10
2x – 10y = – 5
4x – 5y = 4
3x + 5y = 10
– 4x + y = 1
2x + 5y = 3
4x – y = 2
2x + y = 4
r + 2s = – 1
3r – 2s = – 11
2u + 5v = 0
u – v = 7
6x – 2y + 6 = 0
9x + 7y – 31 = 0
4n – 6 = – 10m
15m = 6n + 15
2) Vypočítejte soustavy rovnic o dvou neznámých se zlomky:
3x + 9y = 5
x 3 - y 2 = - 4 9
x 3 - y 2 = - 1 6
x 4 + y 6 = 1 5
4x 5 + y 3 = 1 5
x 4 - y 8 = 0
x 8 - y 3 = - 1 4
x 6 + y 4 = 1 7
x + 3 4 + y - 2 5 = 2 5
3x + 3 7 - y + 1 6 = 5 42
2x - 3 4 + y + 2 3 = 5 2
3x + 2 5 - y - 1 2 = 4
3 4 (x - 4) - y 2 = - 1
7x 4 + 1 6 (y - 1) = 1
8 4 (x - 5) + 2 3 (y + 2) = 0
1 6 (x + 3) - 1 4 (y - 4) = 0
3) Vypočítejte soustavy rovnic o dvou neznámých se závorkami:
(x – 2)(y – 3) = (x + 3)(y – 4)
(x + 4)(y – 4) = (y – 3)(x – 5)
(x + 2)(- y – 1) = – (x + 3)(y – 3)
– 2(x – 1)y = (- 2x – 1)(y + 4)
1 2 (x - 4)(y - 4) = (0,5x - 3)(y - 3)
(4x - 1)(0,5y - 3) = (2x - 2)(y - 3)
(x - 5)(y + 10) = (y - 3)(x - 4) · 2 2
(3 - x)(y - 3) = - (1 + x)(y - 3)
3(x – 4)(x – 1) = (3x + 1)(1 + x)
x = y
4x(y – 5)(y – 3) = x(2y + 3)(2y – 4)
3xy(x – 1) = 3y(x + 1)(x – 4)
10y(x – 1)(x – 5) = y(5x – 3)(2x – 3 + 5)
x – 1 – y + x² = x²