Question

Rozwiąż układ równań.
a)
{2x+y =16
{5x-6y =0

b)
{2(x+y)/3+8=4/3(2x-y)-x-2y/2
{x+1/3+1=3-y/4
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Answer 1

A)
{2x+y =16
{5x-6y =0

y=16-2x
5x-6(16-2x)=0

y=16-2x
5x-96+12x=0

y=16-2x
17x=96

y=16-2x
x=96:12
x=8

y=16-2*8
x=8

y=16-16
x=8
y=0

b)
{2(x+y)/3+8=4/3(2x-y)-x-2y/2
{x+1/3+1=3-y/4(*12)

{(2x+2y)/3+8=(8/3x-4/3y)-x-2y/2(*6)
{x+1/3+1=3-y/4

6(2x+2y)/3+6*8=6(8/3x-4/3y)-6x-6(2y/2)
12x+12/3+12=12(3-y)/4

4x+4y+48=16x-8y-6x-6y
12x+4+12=9-3y

4x+6x-16x=-8y-6y-4y-48
12x+16=9-3y

-6x=-18y-48
12x+16=9-3y

x=3y+8
12(3y+8)+16=9-3y

x=3y+8
36y+96+16=9-3y

x=3y+8
36y+3y=9-112

x=3y+8
39y=103

x=3y+8
y=103:39

x=3y+8
y=2i25/39

x=3(103/39)+8
x=103/13+8
x=7i12/13+8

x=15i12/13
y=2i25/39