b)
\left \{ {{5x+3y=0\ } \atop {-x-2y=7 \ |*5}} \right.
\left \{ {{5x+3y=0} \atop {-5x-10y=35}} \right.
dodaję stronami
5x-5x+5y-10y=0+35
-7y=35 \ |:(-5)
y=-5
podstawiam
-x-2y=7
-x-2*(-5)=7
-x+10=7 \ |-10
-x=-3 \ |*(-1)
x=3
--------
x=3
y=-5
c)
\left \{ {{3u+2v=2 \ |*(-2)} \atop {5u+4v=6 }} \right.
\left \{ {{-6u-4v=-4} \atop {5u+4v=6 }} \right.
dodaję stronami
-6u+5u-4v+4v=-4+6
-u=2 \ |*(-1)
u=-2
3u+2v=2
3*(-2)+2v=2
-6+2v=2
2v=2+6
2v=8 \ |:2
v=4
----------
u=-2
v=4
Zadanie 5
Zadanie 5
b)
\left \{ {{5p-2r=21 \ |*3} \atop {3p+5r=-6 \ \*(-5)}} \right.
\left \{ {{15p-6r=63} \atop {-15p-25r=30}} \right.
-31r=93 \ |:(-31)
r=-3
podstawiam
5p-2r=21
5p-2*(-3)=21
5p+6=21 \ |-5
5p=15 \ |:5
p=3
--------
p=3
r=-3
c)
\left \{ {{2x-3y=10 \ |*5} \atop {5x+5y=0 \ |*(-2}}} \right.
\left \{ {{10x-15y=50} \atop {-10x-10y=0}} \right.
dodaję stronami
-25y=50 \ |:(-25)
y=-2
2x-3y=10
2x-3*(-2)=10
2x+6=10 \ |-6
2x=4 \ |:2
x=2
------------
x = 2
y = -2