Rozwiąż układy równań metodą podstawiania.
a) 2x + 5y = 13
x - 2y = -7
b) -2x + y = 0
3x + 2y = 14
c) -x + 2y = 1
-4x + y = -17
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a)
2x + 5y = 13
x - 2y = -7
2x + 5y = 13
x= - 7 + 2y ( zmieniam kolejność zapisu)
2( 2y - 7) +5y=13
x= 2y - 7
4y-14 + 5y =13
x= 2y - 7
9y= 13 + 14
x= 2y - 7
9y= 27
x= 2y - 7
y= 27 : 9
x= 2y - 7
y= 3
x= 2y - 7
x=2 *3 -7
x= 6 - 7
x= -1
Spr.
L1=2x + 5y =2*( -1) + 5* 3 = -2+15=13
L1=P1
L2=x - 2y = (-1) - 2*3= -1- 6= -7
L2=P2
b)
-2x + y = 0
3x + 2y = 14
y= 0 +2x czyli y= 2x
3x + 2*2x=14
y= 2x
3x + 4x = 14
y= 2x
7x=14
y= 2x
x= 14: 7
y= 2x
x=2
y=2x
y=2*2
y=4
Spr.
L1=-2x + y = -2*2 + 4= -4 + 4=0
L1=P1
L2=3x + 2y =3*2+2*4=6+8 = 14
L2=P2
c)
-x + 2y = 1
-4x + y = -17
-x + 2y = 1
y= 4x - 17
-x + 2* (4x-17) = 1
y= 4x - 17
-x + 8x -34 =1
y= 4x - 17
7x= 1+34
y= 4x - 17
7x=35
y= 4x - 17
x=35:7
y= 4x - 17
x= 5
y= 4x - 17
y= 4*5-17
y=20 -17
y= 3
Spr.
L1=-x + 2y = -5 + 2*3= -5+6= 1
L1=P1
L2=-4x + y = -4*5 + 3= - 20 + 3= -17
L2=P2