Question

1. Rezolvati prin metoda substitutiei sistemele:
a)
{2x+y=0
{x-3y=7.

b)
4x-2y= 0
x-y=-1

c)
2x+3y=3
-x+2y=5

d)
2x-y=1
3x-2y=0

Answer 1

a)
{2x+y=0    y=-2x
{x-3y=7
x-3(-2x)=7
x+6x=7
7x=7
x=1
y=-2

b)
4x-2y= 0
x-y=-1      x=y-1
4(y-1)-2y=0
4y-4-2y=0
2y=4
y=2
x=2-1=1


c)
2x+3y=3
-x+2y=5      x=2y-5
2(2y-5)+3y=3
4y-10+3y=3
7y=13
y=13/7
x=2×13/7 -5 =(26-35)/7=-9/7

d)
2x-y=1      y=2x-1
3x-2y=0
3x-2(2x-1)=0
3x-4x+2=0
x=2
y=2×2-1=4-1=3