Question

1) Rozwiąż układ równań metodą podstawiania i sprawdz, czy znaleziona para liczb spełnia ten układ
a) (2x-5y-6=0
(3x-4y-2=0

b) (3y+5x=0
(3x+2y=0

c) (7x+8y=9
(5x+6y=7

Answer 1

A) (2x-5y-6=0
(3x-4y-2=0

{2x-5y-6=0
{3x=5y+6/ 3

{ 2x-5y-6=0
{x=5/3y+2

{2*(5/3y+2)-5y-6=0
{x=5/3y+2

{10/3y+4-5y-6=0
{x=5/3y+2

{-50/30y-2=0
{x=5/3y+2

{-50/30y=2 / -(50/30)
{x=5/3y+2

{y=-3 1/3
{{x=5/3*10/3+2
{{y=-3 1/3
{{x=5/3*(-10/3)+2=-50/90 +2=1 40/90



B
(3y+5x=0
(3x+2y=0

{3y=-5x/ 3
{3x+2y=0

{y=-5/3x
{3x+2*(-5/3)=0

{{y=-5/3x
{3x-10/3=0

{{{y=-5/3x
{3x=10/3 /3
{x=10
{y=-5/3*10=-50/3

c) (7x+8y=9
(5x+6y=7

{7x=-8y+9
(5x+6y=7
{x=-8/7y+9/7=1/7y
5*1/7+6y=7
5/7+6y=7
x=1/7y
6y=7-5/7
x=1/7y
6y=44/7 /6
{y=37 5/7
{x=1/7*264/7=264/49

Answer 2

A)
2x-5y-6=0
3x-4y-2=0

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

x=5/2y+3
3(5/2y+3)-4y=2

x=5/2y+3
15/2y+9-4y=2

x=5/2y+3
3i1/2y=-7 /:(7/2)

x=5/2y+3
y=-2

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

x=-2
y=-2
SPR
2x-5y-6=0
2*(-2)-5*(-2)-6=0
-4+10-6=0
6-6=0
0=0
L=P
b)3y+5x=0
3y+5x=0
3x+2y=0

3y=-5x/:3
3x+2y=0

y=5/3x
3x+2*5/3x=0

y=5/3x
3x+3i1/3x=0

y=5/3x
6i1/3x=0/:6i1/3

y=5/3x
x=0

y=0
x=0
SPR
3y+5x=0
3*0+5*o=0
0=0
L=P
c)
7x+8y=9
5x+6y=7

7x=9-8y/:7
5x+6y=7

x=9/7-8/7y
5(9/7-8/7y)+6y=7

x=9/7-8/7y
45/7-40/7y+6y=7

x=9/7-8/7y
2/7y=4/7 /:(2/7)

x=9/7-8/7y
y=2

x=-1
y=2
SPR
7x+8y=9
7*(-1)+8*2=9
-7+16=9
9=9
L=P