Rozwiąż układy równań dowolną metodą:
d) 4(x-2)-y = 1
2x - 4y = 8
e) a/3 + b/5 = 7
a/4 - b/5 = 0
f) k/3 + l/4 = 1
k/4 + l/8 = 1
g) 4p/9 - 5r = 1 i 5/6
2p/3 + 2r/3 = -0,1
h) 5x - 5y = 2,5
7y + 3x = 14,5
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d)
{4(x-2)-y = 1
{2x - 4y = 8
{4x-8-y = 1
{2x - 4y = 8
{4x-y = 1+8
{2x - 4y = 8 /·(-2)
{4x-y = 9
{-4x +8y = -16
___________
7y = - 7 /:7
y = - 1
4x-y = 9
4x+1 = 9
4x= 9 - 1
4x = 8 /:2
x = 2
{x = 2
{y = - 1
e)
{a/3 + b/5 = 7 /·15
{a/4 - b/5 = 0 /·20
{5a + 3b = 105
{5a - 4b = 0 /·(-1)
{5a + 3b = 105
{-5a +4b = 0
____________
7b = 105 /:7
b = 15
5a -4b = 0
5a - 4·15 =0
5a -60 = 0
5a = 60 /:5
a = 12
{a = 12
{b = 15
f)
{k/3 + l/4 = 1 /·12
{k/4 + l/8 = 1 /·8
{4k + 3l = 12
{2k + l = 8 /·(-2)
{4k + 3l = 12
{-4k - 2l = -16
___________
l = - 4
2k + l = 8
2k - 4 = 8
2k = 8 + 4
2k = 12 /:2
k = 6
{k = 6
{l = - 4
g)
{4p/9 - 5r = 1⅚
{2p/3 + 2r/3 = -0,1
{4p/9 - 5r = ¹¹/₆ /·18
{2p/3 + 2r/3 = -0,1 /·30
{8p - 90r = 33 /·5
{20p + 20r = -3 /·(-2)
{40p - 450r = 165
{-40p -40r = 6
______________
-490r = 171 /:(-490)
r = - ¹⁷¹/₄₉₀
20p + 20· (- ¹⁷¹/₄₉₀) = -3
20p - ³⁴²/₄₉ = - 3
20p = -¹⁴⁷/₄₉ + ³⁴²/₄₉
20p = ¹⁹⁵/₄₉ /:20
p = ¹⁹⁵/₄₉ · ¹/₂₀
p = ³⁹/₁₉₆
{p = ³⁹/₁₉₆
{r = - ¹⁷¹/₄₉₀
h)
{5x - 5y = 2,5
{7y + 3x = 14,5
{5x - 5y = 2,5 /·(-3)
{3x + 7y = 14,5 /·5
{-15x +15y = -7,5
{15x+ 35y = 72,5
______________
50y = 65 /:50
y = ⁶⁵/₅₀
y = ¹³/₁₀
y = 1,3
5x - 5y = 2,5 /:5
x - y = 0,5
x - 1,3 = 0,5
x = 0,5 + 1,3
x = 1,8
{x = 1,8
{y = 1,3