Question

Rezolvati prin metoda substitutiei urmatoarele sisteme:
a)
{2x-3y=13
{4x+y=5

b) {3x+2y=5
{5x-3y=2

c)
{4x-2y=10
{2x+3y=1

d)
{4x-2y=-2
{3x+y=-9

e)
{4x-3y=6
{5x-7y=1
f)
{x+3y=-1
{2x-y=5

Answer 1

a)
y=5-4x
2x-3(5-4x)=13
2x-15+12x=13
14x=15+13
14x=28 =>x=2
y=5-4·2 =>y=-3

b)3x=5-2y =>x=(5-2y)/3
5(5-2y)/3 - 3y = 2 l·3
25-10y-9y=6
-19y=-19 =>y=1
x=(5-2)/3 =>x=1

c)4x=10+2y l:2 =>2x=5+y =>x=(5+y)/2
5+y+3y=1
4y=-4 =>y=-1
x=(5-1)/2 =>x=2

d)4x=2y-2 l:2 =>2x=y-1 =>x=(y-1)/2
3(y-1)/2 + y = -9  l·2
3y-3+2y=-18
5y=-15 =>y=-3
x=(-3-1)/2 =>x=-2

e)4x=6+3y =>x=(6+3y)/4
5(6+3y)/4 - 7y = 1 l·4
30+15y-28y=4
-13y=-26 =>y=2
x=(6+6)/4 =>x=3

f)x=-1-3y
2(-1-3y)-y=5
-2-6y-y=5
-7y=7 =>y=-1
x=-1+3 =>x=2