Question

Rezolvati prin metoda reducerii sistemele:
a) x+y=5
-x+y=-1
b) 2x-y=3
3x+2y=1

Answer 1

a) {x+y=5
    {-x+y=-1
    /    2y=4
y=4/2
y=2
din x+y=5 avem x+2=5
x=5-2
x=3

b) {2x-y=3      inmultim cu 2
    {3x+2y=1

{4x-2y=6
{3x+2y=1
  7x  /  =7
x=7/7
x=1
din 2x-y=3 avem 2-y=3
-y=3-2
-y=1    inmultim -1
y=-1

Answer 2

y=-1+x
x-1+x=5=>2x=5=1
2x=6=>x=6:2=>x=3
y=-1+3=>y=2

3x+2y=1 I(-1)
-y=3-2x
-3x-2y=-1
-3x-2(3-2x)=-1
-3x-6+4x=-1
x=5
-y=3-10
y=7