Question

8.Rezolvați următoarele sisteme de ecuații:
{(x+3)(2y+5)-2x(y-6)=27
{x(5y-1)-(5x+2)(y+4)=-12

9. Rezolvați sistemele:
{x-2/3+x+y/6=13/6
{2x+1/2- 3x-y/3=3y+11/12

10.Rezolvați următoarele sisteme:
{x+1/y=1/4
{x/y+1=1/5 ; y nu e egal cu-1 , y nu e egal cu 0

Answer 1

8. {(x+3)(2y+5)-2x(y-6) = 27
(x•2y+x•5+3•2y+15+ -2xy + 2x•6) = 27
(2xy-2yx + 12x + 5x + 6y + 15) = 27
(17x+6y+15) = 27
17x + 6y + 15 = 27
17x + 15 = -6y + 27
17x + 6y - 6y + 15 = 27-6y
17x = -6y+12
17x + 15 - 15 = -6y+27-15
17x + 6y + 15 = 27
x = -6y + 12 / 17

{x(5y-1) - (5x+2) (y+4) = -12
(-5xy - 5x • 4 - 2y - 8 + x • 5y - x•1) = -12
(-5yx + 5yx - 20x - x - 2y - 8) = -12
x = -2y - 4 / 21

9. {x - 2/3 + x + y/6 = 13/6
(2x + y/6 - 2/3) = 13/6
12x + y - 4/6 = 13/6
(12x + y - 4) •6 = 6•13/6
12x + y - 4 = 13
(12x+y-4)•6/6 = 6•13/6
12x -4 = -y + 13
12x +y-y-4 = 13-y
12x+y=-4-13
12x = -y+17
12x -4+4=-y+13+4
(x - 2/3+x+y/6) = 13/6
x = -y+17/12

{2x + 1/2 - 3x - y/3 = 3y + 11/12y+(-1x - y/3 + 1/2) = 36y+11 / 12
(-x-y/3+1/2) = 36y+11 / 12
-6x - 2y + 3 / 6 = 36y+11 / 12
(-6x-2y+3)•12 = 6(36y+11)
-6x = 40y+11-6 / 2
-6x -2y+3 = 6•36y+66 / 12
(-6x-2y+3)•12 / 12 = 6(36y+11) / 12
(2x+1/2-3x-y/3) = 3y+11/12
(-1x-y/3+1/2) = 36y+11 / 12
(-x-y/3+1/2) = 36y+11 / 12
-6x -2y+3 / 6 = 36y+11 / 12
(-6x-2y+3)•12 = 6(36y+11)
-6x - 2y + 3 = 216y+66 / 12
-6x -2y+3 = (36y+11) / 2
-6x - 2y + 3 = 36y + 11 / 2
-6x + 3 = 36y + 11 + 4y / 2
-6x = 40y+11-6 / 2

10.
{x+1/y = 1/4
yx+1/y = 1/4
(yx+1)•4=y•1
yx + 1 = y/4
(yx+1)•4/4 = y•1/4
x = y-4/4y

{x/y+1 = 1/5
x+y/y = 1/5
(x+y)•5=y•1
x+y=y/5
(x+y)•5/5=y•1/5
x = -4y/5
(x/y+1) = 1/5
x = y-5y/5
x+y - y = y/5 - y
x = -4y/5.