Question

Rezolvati prin metoda substitutiei sistemele
a)y=2
2x+3y-9=0
b)x=y+2
2x+3y-4=0
c)3a+4b=7
-2a+3b=5
d)2(3x+y)-5=0
x+2y=6

Answer 1

a)
{y=2 |×(-3)
2x+3y-9=0
{-3y=-6
2x+3y=9
2x=15
x=15/2
2x+3y=9
2×15/2+3y=9
30/2+3y=9
15+3y=9
3y=9-15
3y=-6
y=-6/3
y=-2
b)
{x=y+2
2x+3y-4=0
{x-y=2 |×(-2)
2x+3y=4
{-2x+2y=-4
2x+3y=4
5y=0
y=0
-2x+2y=-4
-2x+0=-4
-2x=-4 |:(-2)
x=2
c)
{3a+4b=7 |×2
-2a+3b=5 |×3
{6a+8b=14
-6a+9b=15
17b=29
b=29/17
6a+8b=14
6a+8×29/17=14
6a+232/17=14 |×17
102a+232=238
102a=238-232
102a=6
a=6/102
a=1/17
d)
{2(3x+y)-5=0
x+2y=6
{6x+2y=5
x+2y=6 |×(-1)
{6x+2y=5
-x-2y=-6
5x=11
x=11/5
-x-2y=-6
-11/5-2y=-6 |×5
-11-10y=-30
-10y=-30+11
-10y=-19 |×(-1)
10y=19
y=19/10