Question

Rozwiąż układy równań:
c) (2x - 5)/2 - (x-6)/4=-1,5
(3x-1)/10 + (2y - 5)/5=(2x+y)2

d) (x-3)/5 - (y+1)/2 = 1 - (x - y)
(4x-1)/3 - (y-3)/6= 2(x-y)
Przed każdą parą rownań powinna być klamerka. Z góry dzieki

Answer 1

C) (2x - 5)/2 - (x-6)/4=-1,5 / *4
(3x-1)/10 + (2y - 5)/5=(2x+y)2 / *10

{2(2x-5) - (x-6) = -6
{(3x-1) + 2 (2y-5) = 10(2x+y)2

{4x-10 - x+6 = -6
{3x-1 + 4y-20 = 40x+20y

{4x- x = -6+10 -6
{3x + 4y- 40x-20y =20+1

{3x =10 / :3
{-37x -16y=21

{x =3⅓
{-37x -16y=21

{x =3⅓
{-37* ( 3⅓) -16y=21

{x =3⅓
{-123⅓ -16y=21

{x =3⅓
{ -16y=21+123⅓

{x =3⅓
{ -16y=144⅓ / :(-16)

{x =3⅓
{y=9¹/₄₈



d) (x-3)/5 - (y+1)/2 = 1 - (x - y) / *10
(4x-1)/3 - (y-3)/6= 2(x-y) / *6

{2(x-3) -5 (y+1) = 1*10 - 10(x-y)
{2(4x-1) - (y-3) = 6*2 (x-y)


{2x-6 -5y-5 = 10 - 10x+10y
{8x-2 - y+3 = 12x-12y


{2x -5y +10x-10y = 10+6+5
{8x-y-12x+12y = -3+2

{12x-15y = 21
{-4x+11y = -1 / *3

{12x-15y = 21
{-12x+33y = -3 dodajemy stronami
18y = 18 / 18
y = 1

podstawiamy do pierwszego równania

{12x-15y = 21
12x - 15*1 = 21
12x = 21+15
12x = 36 / 12
x = 3

{x=3
{y=1