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5422a<br />
⎧0,04r+<br />
0,03s = 2,8<br />
⎨<br />
⎩0,02r+<br />
0,05s = 3,5<br />
⎧0,04r<br />
= 2,8 −0,03s<br />
⎨<br />
⎩0,02r+<br />
0,05s− 3,5 = 0<br />
(1) ⎧r<br />
= 70 −0,<br />
75s<br />
⎨<br />
(2) ⎩0,02r+<br />
0,05s− 3,5= 0<br />
() 1 insättes i ( 2)<br />
( )<br />
( div 0,04)<br />
0,02 70 − 0,75s + 0,05s− 3,5 = 0<br />
s = 60<br />
s = 60 insättes i () 1<br />
r = 70 −0,75⋅ 60 = 25<br />
⎧r<br />
= 25<br />
⎨<br />
⎩ s = 60<br />
5422c<br />
⎧1000a=<br />
10b−330 ⎨<br />
⎩100a+<br />
b=<br />
27<br />
(1) ⎧1000a−<br />
10b+ 330 = 0<br />
⎨<br />
(2) ⎩b=<br />
27 −100a<br />
( 2 ) insättes i ( 1)<br />
a ( a)<br />
1000 −10 27 − 100 + 330 = 0<br />
a =−0,03<br />
a =−0,03<br />
insättes i ( 2)<br />
b = 27 −100( − 0,03) = 30<br />
⎧a<br />
=−0,03<br />
⎨<br />
⎩b<br />
= 30<br />
LÖSNINGAR DEL B<br />
( lös själv)<br />
( lös själv)<br />
5422b<br />
⎧0,1x−<br />
0, 25y+ 15 = 0<br />
⎨<br />
⎩0,<br />
2y = 31−0,3x ( div 0, 2)<br />
(1) ⎧0,1x−<br />
0, 25y+ 15 = 0<br />
⎨<br />
(2) ⎩y<br />
= 155 −1,5x<br />
( 2 ) insättes i ( 1)<br />
x ( x)<br />
0,1 −0, 25 155 − 1,5 + 15 = 0<br />
x = 50<br />
x = 50 insättes i () 1<br />
y = 155 −1,5⋅ 50 = 80<br />
⎧x<br />
= 50<br />
⎨<br />
⎩y<br />
= 80<br />
5422d<br />
⎧0,1z−<br />
x+<br />
44 = 0<br />
⎨<br />
⎩0,08z−<br />
x+<br />
50 = 0<br />
⎧−<br />
x=−0,1z−44 ⎨<br />
⎩0,08z−<br />
x+<br />
50 = 0<br />
(1) ⎧x=<br />
0,1 z+<br />
44<br />
⎨<br />
(2) ⎩0,08z−<br />
x+<br />
50 = 0<br />
() 1 insättes i ( 2)<br />
z ( z )<br />
( div − 1)<br />
0,08 − 0,1 + 44 + 50 = 0<br />
z = 300<br />
z = 300 insättes i ( 2)<br />
x = 0,1⋅ 300 + 44 = 74<br />
⎧x<br />
= 74<br />
⎨<br />
⎩<br />
z = 300<br />
( lös själv)<br />
111
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