Question

Rozwiąż układy równań metodą przeciwnych współczynników.

a)
{5x+3y=0
{-x-2y=7

b)
{3u+2v=2
{5u+4v=6

c)
{3s+5t=-6
{1,5s-2t=-3

Answer 1

A)
{5x+3y=0
{-x-2y=7/ *5

5x+3y=0
-5x-10y=35

5x+3y=0
-7y=35/ :(-7)

y=-5
5x=-3y

y=-5
x=3

b)
{3u+2v=2/ * (-2)
{5u+4v=6

-6u-4v=-4
5u+4v=6

-u=2
u=-2

5*(-2)+4v=6
16=4v/ :4

v=4
u=-2

c)
{3s+5t=-6
{1,5s-2t=-3 /* (-2)

3s+5t=-6
-3s+4t=6

t=0

3s+0=-6

s=-2
t=o

Answer 2

A)
{5x+3y=0
{-x-2y=7 |×5
{5x+3y=0
{-5x-10y=35
5x+3y=0
-7y=35 |÷ (-7)

y=-5

5x+3×(-5)=0
5x-15=0 |+15
5x=15 |÷5

x=3

b)
{3u+2v=2 |×(-2)
{5u+4v=6

{-6u-4v=-4
{5u+4v=6
-u=2
u=-2

{3×(-2)+2v=2
-6+2v=2 |+6
2v=8 |÷2
v=4

c)
{3s+5t=-6
{1,5s-2t=-3 |×(-2)

{3s+5t=-6
{-3s+4t=6
9t=0
t=0

3s+5t=-6
3s+5×0=-6
3s=-6 |÷3
s=-2