Matek egyenletrendszer

a,

I. 2x-9y=4 /*9

II. 2y-9x=59 /*2

I. 18x-81y=36

II. 4y-18x=118

I. + II.:

-77y = 154

y = -2

I. `2x-9*(-2)=4`

2x+18=4

2x = -14

x= -7

Megoldás a (-7;-2) számpár.

b,

I. `(3x)/5-(4y)/3=11`

II. `(2x)/15+y/6=-1/3`

I. `(9x-20y)/15=11` /*15

II. `(4x+5y)/30=-1/3` /*30

I. 9x-20y=165

II. 4x+5y=-10 /*4

II. 16x+20y=-40

II. + I.:

25x=125

x = 5

I. `(3*5)/5-(4y)/3=11`

`3-(4y)/3=11`

`(4y)/3=-8`

y = -6

Megoldás a (5;-6) számpár.

c,

I. 2(5x-4y)-3(2x-y)=-8

II. 4(3y-2x)+2(5x-y)=-4

I. 10x-8y-6x+3y=-8

II. 12y-8x+10x-2y=-4

I. 4x-5y=-8

II. 2x+10y=-4 /*2

II. 4x+20y=-8

I. - II:

-25y = 0

y = 0

4x-5*0=-8

4x=-8

x = -2

Megoldás a (-2;0) számpár.

Egyenlő együtthatók módszere
`{(2x,-,9y,=,4),(2y,-,9x,=,59):}``=>``{(2x,-,9y,=,4),(-9x,-,2y,=,59):}``=>``{(18x,-,81y,=,36),(-18x,+,4y,=,118):}`

`18x-81y+(-18x)+4y=36+118`

`-77y=154`

`y=-2`


`2x-9*(-2)=4`

`x=-7`


`(x,y) =(-7,-2)`

b.)
`{((3x)/5,-,(4y)/3,=,11),((2x)/15,+,y/6,=,-1/3):}``=>``{(9x,-,20y,=,165),(4x,+,5y,=,-10):}``=>``{(9x,-,20y,=,165),(16x,+,20y,=,-40):}`

`9x-20y+16x+20y=165+(-40)`

`25x=125`

`x=5`


`4*5+5y=-10`

`y=-6`


`(x,y) =(5,-6)`


c.)
`{(2(5x-4y),-,3(2x-y),=,-8),(4(3y-2x),+,2(5x-y),=,-4):}``=>``{(4x,-,5y,=,-8),(2x,+,10y,=,-4):}``=>``{(4x,-,5y,=,-8),(x,+,5y,=,-2):}`

`4x-5y+x+5y=(-8)+(-2)`

`5x=-10`

`x=-2`



`2*(-2)+10y=-4`

`y=0`

`(x,y) =(-2,0)`