Question

mam problem z 2 układami równań:

a) {1/2x-2y=-5

{3x-1/2y=9/2

b) {1/3x+1/4y=23/12

{2/3x-3/2y=37/6

Answer 1

a)

(1/2) x - 2y = - 5

3x - (1/2) y = 9/2

----------------------

Mnożymy oba równania obustronnie przez 2

x - 4y = - 10  => x = 4y - 10

6x - y = 9

---------------

6*( 4y - 10) - y = 9

24y - 60 - y =  9

23y = 60 + 9

23 y = 69 / : 23

y = 69/23

=========

x = 4*(69/23) - 10 = 276/23 - 230/23 = 46/23 = 2

===========================================

 

b)

(1/3)x + (1/4)y =  23/12  / * 12

(2/3)x - (3/2) y = 37/6     / * 6

------------------------------

4x + 3y = 23

4x - 9y = 37

------------------  odejmujemy stronami

3y - ( -9y) = 23 - 37

12y = - 14  / : 12

y = - 14/12 = - 7/6

===================

4x = 23 - 3y

4x = 23 - 3*( - 7/6) = 23 + 21/6 = 138/6 + 21/6 = 159/6   / : 4

x = 159 /24

x = 6  15/24

x = 6  5/8

===========

Answer 2

a)

(1/2) x - 2y = - 5

3x - (1/2) y = 9/2

----------------------

Mnożymy oba równania obustronnie przez 2

x - 4y = - 10  => x = 4y - 10

6x - y = 9

---------------

6*( 4y - 10) - y = 9

24y - 60 - y =  9

23y = 60 + 9

23 y = 69 / : 23

y = 69/23

=========

x = 4*(69/23) - 10 = 276/23 - 230/23 = 46/23 = 2

===========================================

 

b)

(1/3)x + (1/4)y =  23/12  / * 12

(2/3)x - (3/2) y = 37/6     / * 6

------------------------------

4x + 3y = 23

4x - 9y = 37

------------------  odejmujemy stronami

3y - ( -9y) = 23 - 37

12y = - 14  / : 12

y = - 14/12 = - 7/6

===================

4x = 23 - 3y

4x = 23 - 3*( - 7/6) = 23 + 21/6 = 138/6 + 21/6 = 159/6   / : 4

x = 159 /24

x = 6  15/24

x = 6  5/8

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