Question

Rezolvati prin metoda substitutiei urmatoarele sisteme:
a) {x+y= 10
{2x-y=8.

b)
{x+y=1
{x+2y=-1

c)
{x-2y=-1
{2x-y=7

d)
{x+3y=1
{2x+y=7

Answer 1

a) x=10-y
2 (10-y)=8

x=10-y
20-2y=8

x=10-y
20-8=2y

y=8, x=2
S={(2; 8)}
b) x=1-y
1-y+2y=-1

x=1-y
y=-2

x=3 S={(3;-2)}
c) x=-1+2y
2x-y=7

x=-1+2y
2 (-1+2y)-y=7

x=-1+2y
-2+4y-y=7

x=-1+2y
3y=9

y=3; x=5 S={(5; 3)}
d) x=1-3y
2 (1-3y)+y=7

x=1-3y
2-6y+y=7

x=1-3y
-5y=5

y=-1, x=4 S={(4; -1)}