Question

a)
{2x-3y=13
{4x+y=5

b){4x-3y=6
{5x-7y=1

c)
{x+3y=-1
{2x-y=5

Answer 1

a)

{2 x - 3 y = 13

{4 x + y = 5 ⇒ y = 5 - 4 x

_______________________

2 x - 3 ( 5 - 4 x ) = 13

2 x - 15 + 12 x = 13

14 x = 13 + 15

x = 28 : 14

x = 2

y = 5 - 4 × 2

y = 5 - 8

y = - 3

Verific: 2 × 2 - 3 × ( - 3) = 4 + 9 = 13

b)

{4 x - 3 y = 6 l ×5

{5 x - 7 y = 1 l ×4

___________________

20 x - 15 y = 30 → le scad

20 x - 28y = 4

_________________

/ 13 y = 26

y = 26 /13

y = 2

5 x - 7 y = 1

5 x - 7 × 2 = 1

5 x = 1 + 14

x = 15 : 5

x = 3

c)

{x + 3 y = - 1

{ 2 x - y = 5

___________

x = - 1 - 3 y

2 ( - 1 - 3 y ) - y = 5

- 2 - 6 y - y = 5

- 7 y = 5 + 2

y = 7 : ( - 7)

y = - 1

x = - 1 - 3 ( - 1) = - 1 + 3

x = 2