Question

Bardzo proszę was o rozwiązanie tych zadań
(ze sprawdzeniem)
rozwiąż układy równań metodą podstawiania:
a)
7x+8y=9
5x+6y=7

b)
y+5x-7=0
x+2y=5

Answer 1

A)
7x+8y=9 wyznaczamy x 7x = 9 - 8y stąd x = (9 - 8y)/7 wstawiamy do drugiego
5x+6y=7
5(9 - 8y)/7 + 6y = 7
5(9 - 8y) + 42y = 49
45 - 40y + 42y = 49
2y = 49 - 45
2y = 4
y = 4/2 = 2
7x + 8y = 9
7x + 8 razy 2 = 9
7x + 16 = 9
7x = 9 - 16 = - 7
x = - 7/7 = - 1
x = - 1 , y = 2
sprawdzenie
7x + 8y = 9
7 razy - 1 + 8 razy 2 = 9
- 7 + 16 = 9
9 = 9
L = P
5x + 6y = 7
5 razy - 1 + 6 razy 2 = 7
- 5 + 12 = 7
7 = 7
L = P
b)
y+5x-7=0 wyznaczamy y = 7 - 5x i wstawiamy do drugiego
x+2y=5
x + 2(7 - 5x) = 5
x + 14 - 10x = 5
- 9x = 5 - 14
- 9x = - 9
x = 9/9 = 1
x + 2y = 5
1 + 2y = 5
2y = 5 - 1 = 4
y = 4/2 = 2
x = 1 , y = 2
sprawdzenie
y + 5x = 7
2 + 5 razy 1 = 7
2 + 5 = 7
7 = 7
L = P
x + 2y = 5
1 + 2 razy 2 = 5
1 + 4 = 5
5 = 5
L = P

Answer 2

A)
7x+8y=9 /*5
5x+6y=7 /*7

35x+40y = 45
35x+42y = 49

35x = 45-40y
45-40y+42y = 49
2y = 4 /2

y=2
x=(-1)

spr. 8*2+7(-1) = 16-7 = 9
6*2+5(-1) = 12-5 = 7

b)
y+5x-7=0
x+2y=5

x = 5-2y
y+5(5-2y) = 7
y+25-10y = 7
-9y = -18 /(-9)

y = 2
x = 1

spr. 2+5*1 = 2+5 = 7
1+2*2 = 1+4 = 5