Zadanie Rozwiąż układy równań.
a) \frac{1}{2} x + \frac{1}{2} y= \frac{1}{2} 3x+y=-1
b) \frac{x+2}{3} = \frac{y-5}{-4} 3x+2y=6
c) \frac{x-2}{3} + \frac{y+1}{2} = 2 x-3y=2
d) 2x-y=4 \frac{x-3}{4} = \frac{y-2}{5}
źródło:
a)
\left \{ {{ \frac{1}{2} x+ \frac{1}{2}y= \frac{1}{2} }} |*2\atop { 3x+y=-1 }} \right.
\left \{ {{ x+ y= 1 } \atop {3x+y=-1}} \right.|Odejmuje stronami
x-3x=1-(-1)
-2x=2|/(-2)
x=-1
3*(-1)+y=-1
-3+y=-1
y=-1+3
y=2
b)
\left \{ {{\frac{x+2}{3}=\frac{y-5}{-4}}|*12 \atop {3x+2y=6}} \right. \left \{ {{-4(x+2)=3(y-5)} \atop {3x+2y=6}} \right. \left \{ {{-4x-8=3y-15}|*2 \atop {3x+2y=6}|*3} \right. \left \{ {{-8x-6y=16-30} \atop {9x+6y=18}} \right. -8x+9x=-14+18 x=4 3*4+2y=6 2y=6-12 y=-3
c)
\left \{ {{\frac{x-2}{3}+\frac{y+1}{2}=2}|*6 \atop {x-3y=2}} \right.
\left \{ {{2x-4+3y+3=12} \atop {x-3y=2}} \right.
\left \{ {{2x+3y=13} \atop {x-3y=2}} \right.|Dodaje stronami
2x+x=13+2
3x=15
x=5
5-3y=2
-3y=-5+2
-3y=-3
y=1
d)
\left \{ {{2x -y=4} |*(-4)\atop {\frac{x-3}{4}=\frac{y-2}{5}|*20}} \right. \left \{ {{-8x +4y=-16}\atop {5x-15=4y-8}} \right. \left \{ {{-8x +4y=-16}\atop {5x-4y=15-8}} \right.|Dodaje stronami -8x+5x=-16+7 -3x=-9 x=3 2*3 -y=4 -y=4-6 y=2