ա) 3x — 9 — 1 = 10 — 2x
3x — 3y — 7y = -10
5x = 20
x = 4
12 — 10y = -10
10y = 22
y = 2.2
(4 ; 2.2)
բ) 2x — 2y + 3y + 21 = 16
8x — 3x + 5 = -6 — y — 3
2x + y = -5
y = -14 — 5x
2x — 14 — 5x = -5
-3x = 9
x = -3
y = -14 — 5 (-3) = 1
(-3 ; 1)
գ) 3m — 6 = 4n + 5
5n = m + 1
m = 5n — 1
3 (5n — 1) — 6 — 4n = 5
15n — 3 — 6 — 4n = 5
11n = 14
n = 14/11 = 1.3
m = 5 (1.3) — 1 = 6.5 — 1 = 5.5
դ) 3a + 3 = 3 — 2b
4b + 8 = 6 — 5a
2b = — 3a
b = -3a/2
4 (-3a/2) + 8 — 6 + 5a = 0
-6a + 8 — 6 + 5a = 0
a = -2
b = -3 x (-2)/2 = 3
ե) 3x + 9x — 45 = 38y + 1
8x — 24y + 5y = 7x — 12
x = 19y — 12
12x — 38y = 46
12 (19y — 12) — 38y = 46
228y — 144 — 38y = 46
190y = 186
y = 0.97 = 1
x = 19 x 1 — 12 = 19 — 12 = 7
(7 ; 1)
զ)
y — 1 = 6x + 6y
7y + 28 — y — 2 = 0
5y = -6x — 1
6y = -26
y = -4.3
6x = -1 — 5y
6x = -1 — 5 (-4.3) = -1 + 21.5 = 20.5
x = 3.4
(3.4 ; -4.3)
ա) 2x + y = 11
3x — y = 9
y = 3x — 9
2x + 3x — 9 = 11
5x = 20
x = 4
y = 3 x 4 — 9 = 12 — 9 = 3
(4 ; 3)
բ) 5x — y = 11
4x + 3y = 24
y = 5x — 11
4x + 3 (5x — 11) = 24
4x + 15x — 33 = 24
19x = 57
x = 3
y = 5 x 3 — 11 = 15 — 11 = 4
(3 ; 4)
գ) 2x — 7y = 4
x = y
2y — 7y = 4
-5y = 4
y = -0.8
x = -0.8
(-0.8; -0.8)
դ) x — 10 = 20
-6x + y = -111
x = 20 + 10 = 30
-6 x 30 + y = -111
y = -111 + 180 = 69
(30; 69)
ա) x = 3y — 1
-8 (3y — 1) + 5y = -2
-24y + 8 + 5y = -2
-19y = -10
y = 10/19 = 0.5
x = 3 x 0.5 — 1 = 1.5 — 1 = 0.5
(0.5 ; 0.5)
բ) 5x = -15
x = -3
2z — 3 (-3) = 13
2z = 4
z = 4/2 = 2
(-3 ; 2)
գ) -2x = -3y — 7
x = 1.5y + 3.5
6 (1.5y + 3.5) — 9y = 9
9y + 21 — 9y = 9
0 = 9 — 21
0 = -12
Լուծում չկա
դ) 3u = 1 — 7v
14v + 2 (1 — 7v) = 5
14v + 2 — 14v = 5
0 = 3
Լուծում չկա
ե) 1.2y = 1.5x + 0
y = 1.25x
3.4 x 1.25x + 1.2x = 10.9
4.25x + 1.2x = 10.9
5.45x = 10.9
x = 2
y = 1.25 x 2 = 2.5
(2 ; 2.5)
զ) a = 0.3b + 0.1
1.5 (0.3b + 0.1) + 0.4b = 2.7
0.45b + 0.15 + 0.4b = 2.7
0.85b = 2.55
b = 3
a = 0.3 x 3 + 0.1 = 1
(1 ; 3)
x — փոքր
4.6x — մեծ
x + 4.6x = 56
5.6x = 56
x = 10
4.6x = 4.6 x 10 = 46
Ավտոբուս — x
Գնացք — y
{ x + 2y = 220
{ 3x + 5y = 580
x = 220 — 2y
3 (220 — 2y) + 5y = 580
660 — 6y + 5y = 580
-y = -80
y = 80
x = 220 — 2 x 80 = 220 — 160 = 60
(60 ; 80)
I բանվոր — 1 օր = 1/x աշխատանք
II բանվոր — 1 օր = 1/y աշխատանք
{ 5 (1/x + 1/y) = 1 x 45/100
{ 3 1/x + 4 1/y = 1 x 32/100
1/x + 1/y = 45/5 x 100
1/x + 1/y = 9/100
1/x = 9/100 — 1/y
3 x 9/100 — 3 x 1/y + 4 x 1/y = 32/100
1/y = 32/100 — 27/100
1/y = 5/100 = 1/20
y = 20
1/x = 9/100 — 1/20
1/x = (9 — 5)/100
1/x = 4/100 = 1/25
x = 25
(25 ; 20)
Ա — x
Լ — y
{ x + y = 55
{ x/2 + y = 4x/2
x = 55 — y
x + 2y = 4x
3x — 2y = 0
3 (55 — y) — 2y = 0
165 — 3y — 2y = 0
5y = 165
y = 33
x = 55 — 33 = 22
(22 ; 33)
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