Rowziaż układ równań:

a)

4x-y=18
5x+2½y=30

b)

√2x+√3y=√3+2
x-2√2y=-√2

c)

3x-2y/5 + 5x-3y/3=x+1
2x-3y/3 + 4x-3y/2=y+1

rozwiązania:
a)x=5, y=2
b) x=√2, y=1
c) x=3, y=2

PATRZ ZAŁĄCZNIK ->

a)
{4x-y=18 //*2½
{5x+2½y=30

{10x-2½y=45
+{5x+2½y=30
-----------------
15x=75//:15
x=5

4x-y=18
4*5-y=18
20-18=y
y=2

{x=5
{y=2

c)
{(3x-2y/5) + (5x-3y/3)=x+1//*15
{(2x-3y/3) + (4x-3y/2)=y+1//*6

{3(3x-2y)+5(5x-3y)=15x+15
{2(2x-3y)+3(4x-3y)=6y+6

{9x-6y+25x-15y=15x+15
{4x-6y+12x-9y=6y+6

{34x-15x-21y=15
{16x+3y-6y=6

{19x-21y=15
{16x-3y=6 //*(-7)

{19x-21y=15
+{112x+21y=-42
-----------------------
131x=-27//:131
x=-27/131

Annaa300viz Annaa300viz · Answer 2

a)
{4x-y=18 /razy2½
{5x+2½y=30

{10x-2½y=45
+{5x+2½y=30
metoda przeciwnych wspol dodajemy stronami
15x=75/:15
x=5

4x-y=18
4*5-y=18
20-18=y
y=2

{x=5
{y=2

b)
{√2x+√3y=√3+2
{x-2√2y=-√2

{√2x+√3y=√3+2
{x=2√2y-√2

{√2(2√2y-√2)+√3y=√3+2
{x=2√2y-√2

{4y-2+√3y=√3+2
{x=2√2y-√2

{4y+√3y=√3+2+2
{x=2√2y-√2

{(4+√3)y=4+√3 /:(4+√3)
{x=2√2y-√2

{y=1
{x=2√2raz1-√2=√2

c)
{(3x-2y/5) + (5x-3y/3)=x+1/razy15
{(2x-3y/3) + (4x-3y/2)=y+1/razy6

{3(3x-2y)+5(5x-3y)=15x+15
{2(2x-3y)+3(4x-3y)=6y+6

{9x-6y+25x-15y=15x+15
{4x-6y+12x-9y=6y+6

{34x-15x-21y=15
{16x-15y-6y=6

{19x-21y=15
{16x-21y=6 /(-1)

{19x-21y=15
{-16x+21y=-6
----------------------
3x=9
x=3

16razy 3 -21y=6
-21y=6-48/:(-21)
y=2