Question

Rezolvati prin metoda substitutiei urmatoarele sisteme:
a)
{2x-9y=-1
{-10x-7y+2

b) {3x-6y+3=0
{x+9y=-4

c)
{4a-b=9
{-6a+9b=-3

Answer 1

a)

2x - 9y = -1 (×5)

-10x - 7y = 2

10x - 45y = -5 => 10x = -5 + 45y

-(-5 + 45y) - 7y = 2

5 - 45y - 7y = 2

-52y = 2- 5

-52y = -3

y = 3/52

2x - 9(3/52) = -1

2x - 27/52 = -1

2x = - 52/52 + 27/52

2x = -25/52

x = -25/104

b)

3x - 6y = -3

x + 9y = -4 => x = -4 - 9y

3(-4 - 9y) - 6y = -3

-12 - 27y - 6y = -3

-33y = -3 + 12

-33y = 9

y = -9/33

x = -4 - 9(-9/33)

x = -4 + 81/33

$x = - \frac{132}{33} + \frac{81}{33}$

$x = - \frac{51}{33}$

c)

4a - b = 9 => 4a - 9 = b

-6a + 9b = -3

-6a + 9(4a - 9) = -3

-6a + 36a - 81 = -3

30a = -3 + 81

30a = 78

a = 2,6

b = 4(2,6) - 9

b = 10,4 - 9

b = 1,4