Zadanie 10.6
a) {1,5 - (x - y) = 0,5(y - x) + 2
{2y - 4 = 4x|: 2
{1,5 - (x - y) = 0,5(y - x) + 2
{y = 2x + 2
{1,5 - (x - (2x + 2)) = 0,5(2x + 2 - x) + 2
{y = 2x + 2
{1,5 - (-x -2x - 2) = 0,5(x + 2) + 2
{y = 2x + 2
{1,5 - (-x - 2) = 0,5x + 1 + 2
{y = 2x + 2
{1,5 + x + 2 = 0,5x + 1 + 2
{y = 2x + 2
{x - 0,5x = 3 - 2 - 1,5
{y = 2x + 2
{0,5x = -0,5|: (0,5)
{y = 2x + 2
{x = -1
{y = 2*(-1) + 2
{x = -1
{y = 0
b) {x + y = 0
{[tex]\frac{x+2}{4}[/tex] - [tex]\frac{y-3}{3}[/tex] = [tex]\frac{1}{4}[/tex]
{x = -y
{[tex]\frac{x+2}{4}[/tex] - [tex]\frac{y-3}{3}[/tex] = [tex]\frac{1}{4}[/tex]
{x = -y
{[tex]\frac{-y+2}{4}[/tex] - [tex]\frac{y-3}{3}[/tex] = [tex]\frac{1}{4}[/tex]
{x = -y
{[tex]\frac{-y+2}{4}[/tex] - [tex]\frac{y-3}{3}[/tex] = [tex]\frac{1}{4}[/tex]|* 12
{x = -y
{3(-y + 2) - 4(y - 3) = 3
{x = -y
{-3y + 6 - 4y + 12 = 3
{x = -y
{-3y + 6 - 4y + 12 = 3
{x = -y
{-3y - 4y = 3 - 6 - 12
{x = -y
{-7y = -15|: (-7)
{x = -y
{y = [tex]\frac{15}{7}[/tex]
{x = -[tex]\frac{15}{7}[/tex]
{y = [tex]\frac{15}{7}[/tex]
c) {[tex]\frac{3x - y}{2}[/tex] - [tex]\frac{x+4}{4}[/tex] = 4|* 4
{[tex]\frac{x-y}{2}[/tex] - [tex]\frac{x+5y}{5}[/tex] = 5
{2(3x - y) - (x+1) = 16
{[tex]\frac{x-y}{2}[/tex] - [tex]\frac{x+5y}{5}[/tex] = 5
{6x - 2y - x - 1 = 16
{[tex]\frac{x-y}{2}[/tex] - [tex]\frac{x+5y}{5}[/tex] = 5
{5x = 17 + 2y|: 5
{[tex]\frac{x-y}{2}[/tex] - [tex]\frac{x+5y}{5}[/tex] = 5
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{[tex]\frac{x-y}{2}[/tex] - [tex]\frac{x+5y}{5}[/tex] = 5
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{[tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y - y/2 -
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{[tex]\frac{17 - 3y}{5}[/tex]/2 - [tex]\frac{17 + 27y}{5}[/tex]/5 = 5
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{[tex]\frac{17 - 3y}{10}[/tex] - [tex]\frac{17 + 27y}{25}[/tex] = 5|* 50
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{5(17 - 3y) - 2(17 + 27y) = 250
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{85 - 15y - 34 - 54y = 250
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{-69y = 250 - 51
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{-69y = 199|: (-69)
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex]y
{y = -[tex]\frac{199}{69}[/tex]
{x = [tex]\frac{17}{5}[/tex]+ [tex]\frac{2}{5}[/tex] * ( -[tex]\frac{199}{69}[/tex])
{y = -[tex]\frac{199}{69}[/tex]
{x = [tex]\frac{17}{5}[/tex]- [tex]\frac{398}{345}[/tex]
{y = -[tex]\frac{199}{69}[/tex]
{x = [tex]\frac{1173}{345}[/tex] - [tex]\frac{398}{345}[/tex]
{y = -[tex]\frac{199}{69}[/tex]
{x = [tex]\frac{775}{345}[/tex]
{y = -[tex]\frac{199}{69}[/tex]
{x = [tex]\frac{155}{69}[/tex]
{y = -[tex]\frac{199}{69}[/tex]
d) {7x - 3y = [tex]\frac{-5(x+y)}{2}[/tex] - [tex]\frac{5y-25x}{3}[/tex]
{3[tex]\sqrt{2}[/tex]x + 3
{7x - 3y = [tex]\frac{-5(x+y)}{2}[/tex] - [tex]\frac{5y-25x}{3}[/tex]
{3[tex]\sqrt{2}[/tex]x = - 3
{7x - 3y = [tex]\frac{-5(x+y)}{2}[/tex] - [tex]\frac{5y-25x}{3}[/tex]
{x = -y
{7*(-y) - 3y = [tex]\frac{-5(-y+y)}{2}[/tex] - [tex]\frac{5y-25*(-y)}{3}[/tex]
{x = -y
{-10y = [tex]\frac{-5(0)}{2}[/tex] - [tex]\frac{5y+25y}{3}[/tex]
{x = -y
{-10y = [tex]\frac{0}{2}[/tex] - [tex]\frac{5y+30y}{3}[/tex]
{x = -y
{-10y = - 10y|: (-10)
{x = -y
{y ∈ R
{x = -y
