Question

4) Rezolvați prin metoda substituției sistemele:

a) -2x+y=2
3x+5y=10

b) x-3y=2
4x+5y=25

c) 4x-3y=18
5x-2y=19

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

e) 6x-7y=18
2x+5y=6

f) x-2y=8
4x +5y=6

g) 2x+5y=-11
-6x+y=47

h) 2x+4y=6
x-y=9​

Answer 1

Explicație pas cu pas:

a)y=2+2x

3x+5(2+2x)=10 ; 3x+10+10x=10 ; 13x=0 ; x=0 =>y=2

b)x=2+3y

4(2+3y)+5y=25 ; 8+12y+5y=25 ; 17y=17 ; y=1 =>x=5

c)x=(18+3y)/4

5(18+3y)/4 - 2y = 19 ; 90+15y-8y=76 ; 7y=(-26) ; y=(-26/7) =>x=(18 - 78/7)/4 ; x=12/7

d)x=(9+4y)/5

3(9+4y)/5 + 2y = 1 ; 27+12y+10y=5 ; 22y=(-22) ; y=(-1) =>x=1

e)x=(18+7y)/6

2(18+7y)/6 + 5y = 6 ; 18+7y+15y=18 ; 22y=0 ; y=0 =>x=3

f)x=8+2y

4(8+2y)+5y=6 ; 32+8y+5y=6 ; 13y=(-26) ; y=(-2) =>x=4

g)x=(-11-5y)/2

-6(-11-5y)/2 + y = 47 ; 33+15y+y=47 ; 16y=14 ; y=7/8 =>x=(-11-5•7/8)/2 ; x=(-11-35/8)•1/2 ; x=(-8)

h)x+2y=3 =>x=3-2y

3-2y-y=9 ; -3y=6 ; y=(-2) =>x=7