Rozwiąż układy równań metodą przeciwnych współczynników :
d) 2x - 3y = 7
3x - 5y = 11
e) 5p - 2r = 21
3p + 5r = -6
f) 2x - 3y = 10
5x + 5y = 0
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d) 2x - 3y = 7 /* (-1,5)
3x - 5y = 11
-3x +4,5y = -10,5
3x - 5y = 11
-3x + 4,5y + 3x - 5y = -10,5 + 11
-0,5y = 0,5 /: (-0,5)
y= -1
2x - 3y = 7
2x - 3(-1)= 7
2x +3 = 7
2x = 7-3
2x = 4/:2
x= 2
e) 5p - 2r = 21 /*2,5
3p + 5r = -6
12,5p - 5r = 52,5
3p + 5r = -6
12,5p - 5r + 3p + 5r = 52,5 - 6
15,5 p= 46.5 /: 15,5
p= 3
5p - 2r = 21
15 - 2r= 21
-2r = 21 - 15
-2r = 6 /: (-2)
r= - 3
f) 2x - 3y = 10 /* (-2,5)
5x + 5y = 0
-5x +7,5y = -25
5x + 5y = 0
-5x + 7,5y + 5x + 5y = -25 + 0
12,5y = -25 /: 12,5
y= -2
2x - 3y = 10
2x - 3* (-2) = 10
2x + 6 = 10
2x = 10 - 6
2x = 4 /:2
x= 2
Pozdrawiam, Damiankw :)
d)
2x - 3y = 7 / ×(-3)
3x - 5y = 11 / ×2
-6x + 9y = -21
6x - 10y = 22
-y = 1
y = -1
2x + 3 = 7
2x = 4
x = 2
e)
5p - 2r = 21 /×5
3p + 5r = -6 /×2
25p -10r = 105
6p + 10r = -12
31p = 93
p = 3
9 + 5r = -6
5r = -15
r = -3
f)
2x - 3y = 10 /×(-5)
5x + 5y = 0 /×2
-10x + 15y = -50
10x + 10y = 0
25y = -50
y = -2
2x + 6 = 10
2x = 4
x = 2
Proszę :)