Rozwiązywanie układów równań
2x+5y=8
x+3y=4
najpierw metodą podstawiania, a następnie metodą przeciwnych współczynników.
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1)
2x + 5y= 8
x + 3y = 4 --> x = 4 - 3y
-------------------
2*(4 - 3y) + 5y = 8
8 - 6y + 5y = 8
- y = 0
y = 0
===
x = 4 -3*0 = 4 - 0 = 4
Odp. x = 4 ; y = 0
======================
2)
2x + 5y = 8
x + 3y = 4 / * (-2)
----------------------------
2x + 5y = 8
-2x -6y = - 8
-------------------- dodajemy stronami
-y = 0
y = 0
====
2x + 5y = 8 / * (-3)
x + 3y = 4 / * 5
---------------------------
-6x - 15y = - 24
5x + 15 y = 20
--------------------- dodajemy stronami
-x = - 4
x = 4
=====
Odp. x = 4 ; y = 0
--------------------------------------------------------------------------
2x+5y = 8
x+3y = 4
Metoda podstawiania:
2x+5y = 8
x+3y = 4
2x+5y = 8
x = 4-3y
2(4-3y) +5y = 8
x = 4-3y
8-6y+5y = 8
x = 4-3y
-y = 8-8
y = 0
x = 4-3*0 = 8
x = 8-4
x = 4
{x = 4}
{y = 0}
Metoda przeciwnych współczynników:
2x+5y = 8
x+3y = 4 I*(-2)
2x+5y = 8
-2x-6y = -8
--------------
+
y = 0
x+3*0 = 4
x = 4
{x = 4}
{y = 0}