Question

Ratunku !!!! zad 10 str 97

Answer 1

A) {x/2+y/3=1⅓ |*6
{x/3-y/2=2⅓ |*6

{3x+2y=8 |*3
{2x-3y=14 |*2

{9x+6y=24
{4x-6y=28 (dodajemy górę i dół)

13x=52 |:13
x=4
9*4+6y=24
36+6y=24
6y=-12 |:6
y=-2
Odp. x=4, y=-2

b) {3/5x+1/2y=2 |*10
{1/2(2x-y)=2

{6x+5y=20
{x-1/2y=2 |*6

{6x+5y=20
{6x-3y=12 (odejmujemy dół od góry)

8y=8 |:8
y=1
6x-3=12
6x=15 |:6
x=2,5
Odp. y=1 x=2,5

c) {x+2 /5 -2y=5 |*5
{x- y+2 /6=3 |*6

{x+2-10y=25 -> x-10y=23 |*6
{6x-y+2=18 -> 6x-y=16

{6x-60y=138
{6x-y=16 (odejmujemy)

-61y=122 |: (-61)
y=-2
6x+2=16
6x=14 |:6
x=2⅓

Odp. y=-2 x=2⅓

d) {x+y /2 -x/3=4 |*6
{x-y /2 + y/3=-3 |*6

{3x+3y-2x=24 -> x+3y=24
{3x-3y+2y=-18 -> 3x-y=-18 |*3

{x+3y=24
{9x-3y=-54 (dodajemy)

10x = -30 |:10
x=-3
-3+3y=24
3y=27 |:3
y=9
Odp. x=-3 y=9

e) {3x-1/ 5 +2y-3 /4 = 3(y+1)/2 -> 3x-1/5+2y-3/4=3y+3/2 |*20
{x+y /4 - 3y-1/2 = x-6y/4 |*4

{12x-4+10y-15=30y+30 -> 12x-20y=49
{x+y-6y-2=x-6y -> -2=y

12x+40=49
12x=9 |:10
x=0,75

Odp. y=-2 x=0,75

f) {3x-2/3 -2x+y/6 =x +⅙ |*6
{x+y - -x+y/5 =⅕ -0,8x |*10

{6x-4-2x+y=6x+1 -> -2x+y=5 |*10
{10x+10y+2x-y=2-8x -> 20x+9y=2

{20x+10y=50
{20x+9y=2 (odejmujemy)

y=48
20x+432=2
20x=-430 |:20
x=-21,5

Answer 2

/ kreska ulamkowa
* znak mnozenia
a) x/2 + y/3 = 1 ⅓ | * ½
x/3 - y/2 = 2 ⅓ | * ⅓
x/4 + y/6 = 4/6
x/9 - y/6 = 7/9
-----------------------
x/4 + x/9 = 4/6 + 7/9
9x/36 + 4x/36 = 12/18 + 14/18
13x/36 = 26/18 | * 36/13
x = 4



b)
⅗x + ½ y = 2 | * 10
½(2x-y)=2| * 10
6x + 5y = 20
10x - 5y = 20
16y=20
y = 2,5

⅗ * 2,5 + ½ y = 2
⅗ * 5/2 + ½ y = 2
8/2 + ½ y = 2
½y = - 3/2 + 2 | *2
y = 1