Rozwiązane

Rozwiąż układ równań metodą podstawiania:

a)
{x+3y=5

{x-5y=-3


b)
{2x+y=11

{3x-y=14

Odpowiedź :

123bodzioviz

Odpowiedź:

a)

x+ 3y = 5 ⇒ x = - 3y + 5

x - 5y = - 3

- 3y + 5 - 5y = - 3

- 8y = - 3 - 5

- 8y = - 8

8y = 8

y = 8/8 = 1

x = - 3y + 5 = - 3 * 1 + 5 = - 3 + 5 = 2

b)

2x + y = 11 ⇒ y = - 2x + 11

3x - y = 14

3x - (- 2x + 11) = 14

3x + 2x - 11 = 14

5x = 14 + 11

5x = 25

x = 25/5 = 5

y = - 2x + 11 = - 2 * 5 + 11 = - 10 + 11 = 1

Magdaviz

Odpowiedź:

[tex]a)\\\\\begin{cases}x+3y=5\\x-5y=-3\end{cases}\\\\\\\begin{cases}x=5-3y\\x-5y=-3\end{cases}\\\\\\5-3y-5y=-3\\\\5-8y=-3\\\\-8y=-3-5\\\\-8y-8\ \ /:(-8)\\\\y=1\\\\\\x=5-3\cdot1=5-3=2\\\\\\\begin{cases}x=2\\y=1\end{cases}[/tex]

[tex]b)\\\\\begin{cases}2x+y=11\\3x-y=14\end{cases}\\\\\\\begin{cases}y=11-2x\\3x-y=14\end{cases}\\\\\\3x-(11-2x)=14\\\\3x-11+2x=14\\\\5x=14+11\\\\5x=25\ \ /:5\\\\x=5\\\\\\y=11-2\cdot5=11-10=1\\\\\\\begin{cases}x=5\\y=1\end{cases}[/tex]

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