Răspuns:
Explicație pas cu pas:
a)
x+y=2
x-y=4 (adunam ecuatiile)
x+x+y-y=2+4
2x=6
x=3
y=-1
b)
2x-y=-1
-2x-y=-1 (adunam ecuatiile)
2x-2x-y-y=-1-1
-2y=-2
y=1
x=0
c)
x-2y=-15
x-y=-5 (scadem ecuatiile)
x-x-2y+y=-15+5
-y=-10
y=10
x=5
d)
5x+2y=18
3x-y=2 (inmultim a 2a ecuatie cu 2)
noul sistem
5x+2y=18
6x-2y=4 (adunam ecuatiile)
5x+6x+2y-2y=18+4
11x=22
x=2
y=4
e)
2x-3y=-10 (inmultim cu 6)
3x-2y=-10 (inmultim cu 4)
noul sistem
12x-18y=-60
12x-8y=-40 (scadem ecuatiile)
12x-12x-18y+8y=-60+40
-10y=-20
y=2
x=-2
f)
12x+5y=26 (inmultim cu 3)
10x+3y=24 (inmultim cu 5)
noul sistem
36x+15y=78
50x+15y=120 (scadem ecuatiile)
36x-50x+15y-15y=78-120
-14x=-42
x=3
y=-2
g)
8x+5y=10 (inmultim cu 5)
20x+9y=18 (inmultim cu 2)
noul sistem
40x+25y=50
40x+18y=36 (scadem ecuatiile)
40x-40x+25y-18y=50-36
7y=14
y=2
x=0
h)
18x+25y=-7
9x+19y=-10 (inmultim cu 2)
noul sistem
18x+25y=-7
18x+38y=-20 (scadem ecuatiile)
18x-18x+25y-38y=-7+20
-13y=13
y=-1
x=1
i)
-2x+17y=-30 (inmultim cu 9)
9x-15y=12 (inmultim cu 2)
noul sistem
-18x+153y=-270
18x-30y=24 (adunam ecuatiile)
noul sistem
-18x+18x+153y-30y=-270+24
123y=-246
y=-2
x=-2
