zad1
rozwiąż dowolną metodą algebraiczną układy równań
a)
x+y/3 + y/5 = -2
2x-y/3 - 3x/4 = 3/2
b)
2x-y=4
-4x+2y=6
Metoda podstawiania.a)(x+y)/3 + y/5 = -2 /*15(2x-y)/3 - 3x/4 = 3/2 /*125(x+y) + 3y = -304(2x-y) - 9x = 185x + 5y + 3y = -308x - 4y - 9x = 185x + 8y = -30 -x - 4y = 18 /:(-1)5x + 8y = -30x + 4y = -185x + 8y = -30x = -18 - 4y5(-18 - 4y) + 8y = -30x = -18 - 4y-90 - 20y + 8y = -30x = -18 - 4y-12y = 60 /:(-12)x = -18 - 4yy = -5x = -18 - 4(-5)x = 2y = -5b)2x-y=4-4x+2y=6-y = 4 - 2x /:(-1)-4x + 2y = 6y = -4 + 2x-4x + 2(-4 + 2x) = 6y = -4 + 2x-4x -8 + 4x = 6y = -4 + 2x0 = 14 Układ równań sprzeczny.
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Metoda podstawiania.
a)
(x+y)/3 + y/5 = -2 /*15
(2x-y)/3 - 3x/4 = 3/2 /*12
5(x+y) + 3y = -30
4(2x-y) - 9x = 18
5x + 5y + 3y = -30
8x - 4y - 9x = 18
5x + 8y = -30
-x - 4y = 18 /:(-1)
5x + 8y = -30
x + 4y = -18
5x + 8y = -30
x = -18 - 4y
5(-18 - 4y) + 8y = -30
x = -18 - 4y
-90 - 20y + 8y = -30
x = -18 - 4y
-12y = 60 /:(-12)
x = -18 - 4y
y = -5
x = -18 - 4(-5)
x = 2
y = -5
b)
2x-y=4
-4x+2y=6
-y = 4 - 2x /:(-1)
-4x + 2y = 6
y = -4 + 2x
-4x + 2(-4 + 2x) = 6
y = -4 + 2x
-4x -8 + 4x = 6
y = -4 + 2x
0 = 14 Układ równań sprzeczny.