Question

Witam. Proszę mi pomóc z układami równań ! :) Dziękuje z góry. ( 1 klasa liceum , poziom podstawowy )

a) x+y/2 + 1 = x-y/4
x+y=2
b)2x-y/2 - 1/2 = 3y+2x/2 +8
2x-y = 11
c) 1- x-2y/3 +1 = x -y/2 +1/6
2x-3y = 5
d) x+y/2 - x-y/2 + x = 2x-1/4 - 2y+1/6 - 37/12
2x+3y = -8

PROSZĘ !!!!

Answer 1

A) x+y/2 + 1 = x-y/4 /*4
x+y=2

2x+2y+4=x-y
x=2-y

x+3y=-4
x=2-y

2-y+3y=-4
x=2-y

2y=-6
x=2-y

y=-3
x=5


b)2x-y/2 - 1/2 = 3y+2x/2 +8 / *2
2x-y = 11

2x-y-1=3y+2x+16
2x-y=11

-4y=17
2x-y=11

y=- 17/4
2x-(-17/4)=11

y=- 17/4
2x=6 3/4

y= - 17/4 = - 4 1/4
x= 27/8 = 3 3/8

c) 1- x-2y/3 +1 = x -y/2 +1/6 / * 6
2x-3y = 5

6-2x+4y+6=6x-3y+1
x=3/2y+5/2

-8x+7y=-11
x=3/2y+5/2

-8(3/2y+5/2)+7y=-11
x=3/2y+5/2

-12y-20+7y=-11
x=3/2y+5/2

y= - 9/5
x=3/2 * (- 9/5) + 5/2

y= -9/5 = - 1 4/5
x= - 1/5


d) x+y/2 - x-y/2 + x = 2x-1/4 - 2y+1/6 - 37/12 /* 12
2x+3y = -8

6x+6y-6x+6y+12x=6x-3-4y-2-37
y=- 2/3x-8/3

16y+6x=-42
y=- 2/3x-8/3

16(-2/3x-8/3)+6x=-42
y=-2/3x-8/3

-32/3x-128/3+6x=-42
y= -2/3x-8/3

x= - 1/7
y= -2/3 * (-1/7) - 8/3= - 2 4/7
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