Rozwiązane

Rozwiąż układy równań metodą podstawiania :
A.x+3y=3
x-y=5
B.2x-y=10
x+5y= -17
C.3m+n=9
2m - 5n = -11
D. 4a - 2 = b
3a + 7b = 1,5
E.5x = 4-2y
4x + y = 3
F.6x - 3y = 9
x+5y = -9,5



Odpowiedź :

A.x+3y=3 x-y=5
x=3-3y
3-3y-y=5
3-4y=5
-4y=5-3
y=-2/4=-1/2
x+3*(-1/2)=3
x=3+2/3=3i 2/3

B.2x-y=10 x+5y= -17
x=-17-5y
2*(-17-5y)-y=10
-34-10y-y=10
-11y=44
y=-4
x=-17-5*(-4)
x=-17+20=3

C.3m+n=9 2m - 5n = -11
n=9-3m
2m-5(9-3m)=-11
2m-45+15m=-11
17m=-11+45
17m=34
m=2
n=9-6=3


D. 4a - 2 = b 3a + 7b = 1,5
3a+7(4a - 2)=1,5
3a+28a-14=1,5
31a=1,5+14
31a=15,5
a=0,5
b=4*0,5-2=0

E.5x = 4-2y 4x + y = 3
y=3-4x
5x=4-2(3-4x)
5x=4-6+8x
5x-8x=-2
-3x=-2
x=2/3
y=3-4*2/3=3-(2 i 2/3)=1/3


F.6x - 3y = 9 x+5y = -9,5
x=-9,5-5y
6*(-9,5-5y)-3y=9
-57-30y-3y=9
-33y=9+57
-33y=66
y=-2
x=-9,5-5*(-2)
x=-9,5+10=0,5
x+3y=3
x-y=5
x=3-3y
3-3y-y=5
x=3-3y
-4y=5-3
x=3-3y
-4y=2/:(-4)
x=3-3y
y=-1/2
x=3-3*(-1/2)
y=-1/2
x=3+3/2
y=-1/2
x=4i1/2
y=-1/2
B
2x-y=10
x+5y= -17
x=-17-5y
2(-17-5y)-y=10
x=-17-5y
-34-10y-y=10
x=-17-5y
-11y=10+34
x=-17-5y
-11y=44/:(-11)
x=-17-5y
y=-4
x=-17-5*(-4)
y=-4
x=-17+20
y=-4
x=3

c
3m+n=9
2m - 5n = -11
n=9-3m
2m-5(9-3m)=-11
n=9-3m
2m-45+15m=-11
n=9-3m
17m=-11+45
n=9-3m
17m=34/:17
n=9-3m
m=2
n=9-3*2
m=2
n=9-6
m=2
n=3
m=2
D
4a - 2 = b
3a + 7b = 1,5
b=4a-2
3a+7(4a-2)=1,5
b=4a-2
3a+28a-14=1,5
b=4a-2
31a=1,5+14
b=4a-2
31a=15,50/:31
b=4a-2
a=0,5
b=4*0,5-2
a=0,5
b=0
E
5x = 4-2y
4x + y = 3
y=3-4x
5x=4-2(3-4x)
y=3-4x
5x=4-6+8x
y=3-4x
5x-8x=-2
y=3-4x
-3x=-2/:(-3)
y=3-4x
x=2/3
y=3-4*2/3
x=2/3
y=3-8/3
x=2/3
y=1/3
F
6x - 3y = 9
x+5y = -9,5
x=-9,5-5y
6(-9,5-5y)-3y=9
x=-9,5-5y
-57-30y-3y=9
x=-9,5-5y
-33y=9+57
x=-9,5-5y
-33y=66/:(-33)
x=-9,5-5y
y=-2
x=-9,5-5(-2)
y=-2
x=0,5

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