Odpowiedź:
a)
2x - 8y = 6
3x + y = 2
2x - 8y = 6
y = 2 - 3x
2x - 8(2 - 3x) = 6
y = 2 - 3x
2x - 16 + 24x = 6
y = 2 - 3x
2x + 24x = 6 + 16
y = 2 - 3x
26x = 22
y = 2 - 3x
x = 22 : 26
y = 2 - 3x
x = 22/26
y = 2 - 3x
x = 11/13
y = 2 - 3*11/13
x = 11/13
y = 2 - 33/13
x = 11/13
y = 26/13 - 33/13
x = 11/13
y = - 7/13
spr.
3x + y = 2
L = 3x + y= 3* 11/13 + (-7/13) = 33/13 - 7/13= 26/13= 2
P= 2
2=2
L=P
b)
3x + 2y =9 /*3
- 4x + 3y = - 22 /*2
9x + 6y = 27
- 8x + 6y = - 44
6y = 27 - 9x
- 8x + 6y = - 44
6y = 27 - 9x
-8x + (27 - 9x) = - 44
6y = 27 - 9x
-8x + 27 - 9x = - 44
6y = 27 - 9x
-8x - 9x = - 44 - 27
6y = 27 - 9x
- 17x= - 71
6y = 27 - 9x
x= - 71 : (-17)
6y = 27 - 9x
x= 71/17
6y = 27 - 9x
x= 4 i 3/17
6y = 27 - 9*4 i 3/17
x= 4 i 3/17
6y = 27 - 9*71/17
x= 4 i 3/17
6y = 459/17 - 639/17
x= 4 i 3/17
6y = - 180/17
x= 4 i 3/17
y= - 180/17 : 6
x= 4 i 3/17
y= - 180/17 * 1/6
x= 4 i 3/17
y= - 30/17 * 1/1
x= 4 i 3/17
y= - 30/17
x= 4 i 3/17
y= - 1 i 13/17
x= 4 i 3/17
spr.
3x + 2y =9
L= 3x + 2y = 3*4 i 3/17 + 2*(-1 i 13/17) = 3 * 71/17 - 2*30/17 = 213/17 - 60/17 =
= 153/17 = 9
P= 9
9=9
L=P
c)
7x - 3y = 10
4x + y = 3
7x - 3y = 10
y= 3 - 4x
7x - 3(3 - 4x) = 10
y= 3 - 4x
7x - 9 + 12x = 10
y = 3 - 4x
7x + 12x= 10 + 9
y= 3 - 4x
19x = 19
y= 3 - 4x
x= 19 : 19
y = 3 - 4x
x= 1
y= 3 - 4x
x= 1
y = 3 - 4*1
x= 1
y = 3-4
x= 1
y= - 1
spr.
7x - 3y = 10
L = 7x - 3y = 7*1 - 3(-1) = 7 - (-3) = 7 + 3= 10
P= 10
10=10
L=P
Szczegółowe wyjaśnienie:
