Question

Rezolvati prin metoda substitutiei urmatoarele sisteme:
1. $\left \{ {{x+y=1} \atop{x+2y=-1}} \right.$
2. $\left \{ {{x+3y=1} \atop {2x+y=7}} \right.$
3. $\left \{ {{2x+y=8-2x} \atop {3(x-y)-2y=29}} \right.$
4. $\left \{ {{2(x+3)-3y=2} \atop {5x-3(2y-1)=-4}} \right.$
5. $\left \{ {{4x-3y=13} \atop {2(x-y)+5y=-7}} \right.$

Answer 1

1. x=1-y
1-y+2y=-1; y=-2; x=3

2. x=1-3y
2(1-3y)+y=7; 2-6y+y=7; -5y=5; y=-1
x=1+3; x=4

3. y=8-4x;
3(x-(8-4x))-2(8-4x)=29
3(x-8+4x)-16+8x=29
3x-24+12x-16+8x=29
23x==29+16+24
x=3; y=-4


4. 2x+6-3y=2
    5x-6y+3=-4
2x-3y=-4; y=(4+2x)/3
5x-6y=-7

5x-6[(4+2x)/3]=-7
5x-2(4+2x)=-7
5x-8-4x=-7
x=1
y=2

5. 4x-3y=13; 3y=-13+4x
2x-2y+5y=-7
2x+3y=-7
2x+(-13+4x)=-7
6x=6; x=1
y=-3