a) [tex]\left \{ {{x-2y=8} \atop {x+y=2}} \right.[/tex]
[tex]\left \{ {{x-2y=8} \atop {y=2-x} \right.[/tex]
[tex]\left \{ {{x-2(2-x)=8} \atop {y=2-x}} \right.[/tex]
x - 2(2 - x) = 8
x - 4 + 2x = 8
x + 2x = 8 + 4
3x = 12 /:3
x = 4
y = 2 - x
y = 2 - 4
y = - 2
b) [tex]\left \{ {{3x+2y=4} \atop {3/5x + 2/5y=0.8}} \right.[/tex]
[tex]\left \{ {{3x+2y=4} \atop {3x+2y=4}} \right.[/tex]
[tex]\left \{ {{3x+2y=4} \atop {x=4/3 - 2/3y}} \right.[/tex]
3([tex]\frac{4}{3}[/tex]-[tex]\frac{2}{3}[/tex]y)+2y=4
4-2y+2y=4
-2y+2y=0
y ∈ R
c) [tex]\left \{ {{3x-4y=1} \atop {6x+3y=1}} \right.[/tex]
[tex]\left \{ {{6x=2+8y} \atop {6x+3y=13}} \right.[/tex]
2+8y+3y=13
11y=11 /:11
y=1
3x - 4*1 = 1
3x - 4 = 1
3x = 5 /:3
x = 5/3
d) [tex]\left \{ {{5x-4y=3} \atop {3x+2y=-7}} \right. \\\left \{ {{5x-4y=3} \atop {6x+4y=-14}} \right. \\[/tex]
5x + 6x = 3 + (-14)
11x = -11 /:11
x = -1
5*(-1) - 4y = 3
-5 - 4y = 3
-4y = 8 /:-4
y=-2
e)
[tex]\left \{ {{3x-7y=4} \atop {x=7/3y+1}} \right. \\\left \{ {{3x-7y=4} \atop {3x=7y+3}} \right.[/tex]
7y + 3 - 7y = 4
3 ≠ 4
brak rozwiązań
f) [tex]\left \{ {{-3+b=7} \atop {5a-b=1}} \right.[/tex]
-3a + 5a = 7+1
2a = 8 /:2
a = 4
-3a + b = 7
-3*4 + b = 7
-12 + b = 7
b = 19
g) [tex]\left \{ {{[(x-2)^2-x^2]:4=2-y} \atop {(3x-4)(y-3)=(3y-7)(x-2)}} \right. \\[/tex]
równanie nr 1
[(x-2)² - x²]:4 = 2 - y
[x^2 - 4x + 2 - x^2] : 4 = 2 - y
[tex]\frac{-4x+2}{4} \\\frac{2(-2x+1)}{4} \\\frac{-2x+1}{2}[/tex]
równanie nr 2
(3x-4)(y-3)=(3y-7)(x-2)
3xy - 9x - 4y + 12 = 3xy - 6y - 7x + 14
3xy - 3xy - 9x + 7x - 4y + 6y + 12 - 14 = 0
2x + 2y - 2 = 0
2x + 2y = 2 /:2
x + y = 1
[tex]\left \{ {{-2x+1=4-2y} \atop {x+y=1}} \right.[/tex]
[tex]\left \{ {{-2x+2y=3} \atop {x+y=1}} \right. \\[/tex]
[tex]\left \{ {-2x+2y=3} \atop {2x+2y=2}} \right.[/tex]
4y = 5
y = 5/4
x+y=1
x + 5/4 = 1
x = 1 - 5/4 = 4/4 - 5/4 = -1/4
x = -1/4
