Question

Rozwiąż układy równan:

a) { 2x+5y=15

{3x+8y=-1

b) {3x-y+5

{5x+2y=23

c) {2x+5y=25

{4x+3y=15

d) {6x-7y=40

{5y-2x=-8

Answer 1

a) { 2x+5y=15 /* (-3)

{3x+8y=-1 /*2

 

-6x - 15y = -45

6x +16y = -2

 

y = -47

 

2x + 5*(-47) = 15

2x - 235 = 15

2x = 250 /:2

x = 125

 

 

x=125

y=-47

 

b) {3x-y+5 /*2

     {5x+2y=23

 

6x -2y=10

5x +2y = 23

 

11x = 33 /:11

x=3

 

3*3 -y = 5

-y = -4/:(-1)

y= 4

 

x=11

y=4

 

c) {2x+5y=25 ?*(-2)

    {4x+3y=15

 

-4x - 10y = -50

4x +3y= 15

 

-7y = - 35 ?:(-7)

y=5

 

2x +5*5 = 25

2x = 0

x=0

 

x=9

y=5

 

d) {6x-7y=40

     {5y-2x=-8 /*3

 

6x - 7y = 40

-6x +15y = -24

 

8y = 16 /:8

y = 2

 

6x - 7*2 = 40

6x = 54 /:6

x = 9

 

x=9

y=2

Answer 2

a) { 2x+5y=15

     {3x+8y=-1

 

2x=15-5y

3x+8y=-1

 

{X=(15-5y) /2

{3x+8y=-1

 

3*(15-5y)/2 + 8y=-1

(45-15y)/2 + 8y=-1      /*2

45-15y+16y=-2

45+y=-2     /-45

y=-47

 

X=15-5*(-47) /2

X=15-235 /2

X=-220/2

X=-110

 

 

c) {2x+5y=25

    {4x+3y=15

 

2X=25-5Y

4X+3Y=15

 

X=25-5Y/2

 

4X+3Y=15

4*25-5Y/2 + 3Y=15

50-10Y+3Y=15

50-7Y=15       /-50

-7Y=15-50

-7Y=-35   /:(-7)

Y=5

 

X=25-5*5 /2

X=0/2

X=0

 

 

d) {6x-7y=40

     {5y-2x=-8

 

6X=40+7Y

X=40+7Y / 6

 

5Y-2*(40+7Y/6)=8

5Y-(40+7Y/3) = 8     /*3

15Y-40-7Y=24

8Y-40=24    /+40

8Y=64   /:8

Y=8

 

X=40+7*8 / 6

X=40+56 / 6

X=96/6

X=16