Question

Rozwiąż podane równania metodą podstawiania.
a) y+2-(3-x)=0
x-2=5-(2-y)
b) 3(x-y)+4x=8
3(x-5y)=5-9y
c) 3(2x-1)+4(y-2)=9
2(5x-1)+3y=5(3x+y)+2
d) 2(x+y)-3(x-2y)=-7x-2
5(x+1)-2(3-y)=-4(x+y)
e) 4(x+2)-3(y-1)=x+y-3
3(x-4)-2(y-2)=4(x-y)+4
i są jeszcze klamry ale nie wiem jak je zrobić
jak coś to jest to z książki Matematyka z Plusem 2 gim str 112 zad 10

Answer 1

A) y+2-(3-x)=0
x-2=5-(2-y)

y+2-3+x=0
x-2=5-2+y

y=1-x
x-(1-x) = 3+2
x-1+x=5
2x=6/:2
x=3

y = 1-3
y = -2

b) 3(x-y)+4x=8
3(x-5y)=5-9y

3x-3y+4x=8
3x-15y=5-9y

7x-3y=8
3x-6y=5 / :3

x = (5+6y)/3
7[(5+6y)/3] - 3y = 8
(35+42y)/3 - 3y = 8 / *3
35+42y - 9y = 24
33y = -11 / :33
y = -1/3

x = [5+6*(-1/3)]/3
x = (5-2)/3
x = 3/3
x = 1

c) 3(2x-1)+4(y-2)=9
2(5x-1)+3y=5(3x+y)+2

6x-3+4y-8=9
10x-2+3y=15x+5y+2

6x+4y=20 / :4
-5x - 2y = 4

y = 5 - 1,5x
-5x-2(5-1,5x) = 4
-5x - 10 + 3x=4
-2x=14 / :(-2)
x = -7

y = 5-1,5*(-7)
y = 5+10,5
y = 15,5

d) 2(x+y)-3(x-2y)=-7x-2
5(x+1)-2(3-y)=-4(x+y)

2x+2y-3x+6y=-7x-2
5x+5-6+2y=-4x-4y

6x+8y=-2 / :6
9x+6y=1

x = -1/3-4y/3
x = -(1+4y)/3

9[-(1+4y)/3] + 6y = 1
-3-12y+6y=1
-6y=4 / :(-6)
y = -2/3

x = -[1+4*(-2/3)/3]
x = -[(1-8/3)/3] / *3
3x = -1+8/3 / *3
9x = -3+8
9x = 5 / :9
x = 5/9

e) 4(x+2)-3(y-1)=x+y-3
3(x-4)-2(y-2)=4(x-y)+4

4x+8-3y+3=x+y-3
3x-12-2y+2=4x-4y+4

3x-4y=2
-x+2y=14 / *(-1)

x = -14+2y
3(-14+2y)-4y=2
-42+6y-4y=2
2y=44 / :2
y = 22

x=-14+2*22
x = -14+44
x = 30