Odpowiedź :
Odpowiedź:
a) 2x + 4y = 11 / ×(-3)
⎨3x - 3y = 1,5 / ×2
-6x-12y=-33
⎨6x-6y=3
dodajemy, bo mamy przeciwne współczynniki, otrzymujemy:
-18y = -30 /:(-18)
y = 2 2/3
b)
(5x + 2y)/3 - (2x-1)/2 = 1 /×6
⎨(3-x)/2 - 2y = 3 /×2
2 × (5x +2y) - 3×(2x-1) = 6
⎨ 3 -x - 4y=6
10x + 4y - 3x +4 = 6
⎨-x - 4y = 3
7x + 4y = 2
⎨-x - 4y = 3
dodajemy, otrzymujemy:
6x =5
x = 5/6
Szczegółowe wyjaśnienie:
Odpowiedź:
[tex]a)\\\\\begin{cases}2x+4y=11\\3x-3y=1,5\ \ /:3\end{cases}\\\\\\\begin{cases}2x+4y=11\\x-y=0,5\end{cases}\\\\\\\begin{cases}2x+4y=11\\x=0,5+y\end{cases}\\\\\\2(0,5+y)+4y=11\\\\1+2y+4y=11\\\\6y=11-1\\\\6y=10\ \ /:6\\\\y=\frac{10}{6}\\\\y=\frac{5}{3}\\\\x=0,5+\frac{5}{3}=\frac{1}{2}+\frac{5}{3}=\frac{3}{6}+\frac{10}{6}=\frac{13}{6}\\\\\begin{cases}x=\frac{13}{6}\\y=\frac{5}{3}\end{cases}[/tex]
[tex]b)\\\\\begin{cases}\frac{5x+2y}{3}-\frac{2x-1}{2}=1\ \ /*6\\\frac{3-x}{2}-2y=3\ \ /*2\end{cases}\\\\\\\begin{cases}2(5x+2y)-3(2x-1)=6\\3-x-4y=6\end{cases}\\\\\\\begin{cases}10x+4y-6x+3=6\\-x-4y=6-3\end{cases}\\\\\\\begin{cases}4x+4y=6-3\\-x-4y=3\end{cases}\\\\\\+\begin{cases}4x+4y=3\\-x-4y=3\end{cases}\\---------\\3x=6\ \ /:3\\x=2\\\\\\-2-4y=3\\\\-4y=3+2\\\\-4y=5\ \ /:(-4)\\\\y=-\frac{5}{4}\\\\\begin{cases}x=2\\y=-\frac{5}{4}\end{cases}[/tex]