Sistemi di equazioni di I grado fratte

Sistemi di equazioni di I grado fratte
Algebra
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9 2
⎧ + =4
𝑥𝑥 𝑦𝑦
⎨6 = 2 + 3
⎩𝑦𝑦
𝑥𝑥
4 5
+ =2
𝑥𝑥 𝑦𝑦
⎨10 − 4 = 1
⎩ 𝑦𝑦 𝑥𝑥
⎧
13 3
+ =0
4𝑥𝑥 𝑦𝑦
⎨ 3 +9= 1+ 5
⎩2𝑦𝑦
2 2𝑥𝑥
3
𝑥𝑥 = − ; 𝑦𝑦 = −3
2
8 2
=
𝑥𝑥 𝑦𝑦
𝑦𝑦 + 4
⎨
⎩1 − 𝑥𝑥 − 2 = 0
7
1
; 𝑦𝑦 = 1
4
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
1 1 3
⎧ + =
𝑥𝑥 𝑦𝑦 𝑦𝑦
3
⎨
⎩𝑥𝑥 − 2 = 𝑦𝑦
⎧−
v 3.0
𝑥𝑥 =
𝑦𝑦 + 1
=2
𝑥𝑥
−
3
�
𝑦𝑦 + 1
𝑥𝑥 − 3 =
2
6
9
𝑥𝑥 = 4; 𝑦𝑦 = 5
⎧10 −
⎧
8
𝑥𝑥 = 3; 𝑦𝑦 = 2
𝑥𝑥 = 8; 𝑦𝑦 = 2
𝑥𝑥 + 4
=2
𝑦𝑦 + 4
⎨ 𝑦𝑦 + 5
⎩ 𝑥𝑥 + 3 = −1
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
8𝑥𝑥 + 4𝑦𝑦 + 7
13
=−
4𝑥𝑥 − 9𝑦𝑦 + 1
2
7𝑦𝑦
−
2𝑥𝑥
+
6
3
⎨
=
⎩ 3𝑦𝑦 + 4 − 5𝑥𝑥 11
⎧
𝑥𝑥 = −2; 𝑦𝑦 = −1
8(2𝑦𝑦 − 3𝑥𝑥 + 7) = 7(𝑥𝑥 + 3𝑦𝑦 − 9)
� 𝑥𝑥 − 1 1 9 − 3𝑥𝑥
= −
1 + 𝑦𝑦 2 𝑦𝑦 + 1
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
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Sistemi di equazioni di I grado fratte
Algebra
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v 3.0
𝑥𝑥 + 1 1 − 2𝑦𝑦
𝑦𝑦 − 𝑥𝑥
−
=
6 − 4𝑦𝑦 2𝑦𝑦 − 3 12 − 8𝑦𝑦
4
⎨
𝑦𝑦
=
+ 𝑥𝑥
⎩
3
⎧
𝑥𝑥 = −1; 𝑦𝑦 =
7 − 𝑥𝑥 2 + 3𝑦𝑦
𝑦𝑦 − 2
=
1
−
𝑥𝑥𝑥𝑥 − 𝑥𝑥 2
𝑦𝑦 − 𝑥𝑥
2(4𝑥𝑥 + 𝑦𝑦)
⎨ 6 + 2𝑥𝑥
=
⎩ 2𝑥𝑥 − 1 1 − 4𝑥𝑥 + 4𝑥𝑥 2
⎧
1
3
2
𝑥𝑥 = − ; 𝑦𝑦 = −
3
2(1 + 𝑦𝑦) = 5 − 𝑥𝑥 + 2𝑦𝑦
�1 + 2𝑥𝑥 + 3𝑦𝑦 3𝑥𝑥 + 2𝑦𝑦 + 1
=
2𝑥𝑥 + 3𝑦𝑦
3𝑥𝑥 + 2𝑦𝑦
𝑥𝑥 = 3; y=3
2(𝑥𝑥 + 𝑦𝑦) = 3
�1 𝑦𝑦 + 1 2 𝑦𝑦 − 1 9
4+
4
2−5
=0
𝑥𝑥
𝑥𝑥
10
1
𝑥𝑥 = − ; 𝑦𝑦 = 2
2
2
2
⎧ 5𝑦𝑦 − 12𝑥𝑥 − 12(𝑥𝑥 − 2𝑦𝑦) = 5(6𝑥𝑥 + 4𝑦𝑦 − 16) − 𝑦𝑦 − 42
⎪ 7 − 𝑦𝑦
7 + 𝑦𝑦
𝑦𝑦 2 − 49
⎨ 𝑥𝑥 + 2 𝑦𝑦 − 1 (𝑦𝑦 − 𝑥𝑥)(𝑥𝑥 + 𝑦𝑦) − 3(𝑥𝑥 + 𝑦𝑦) − 4
⎪− 𝑦𝑦 − 1 + 𝑥𝑥 + 2 =
𝑥𝑥𝑥𝑥 − 𝑥𝑥 + 2𝑦𝑦 − 2
⎩
𝑥𝑥 − 3𝑦𝑦
5
⎧
= −
2𝑥𝑥 + 𝑦𝑦
4
⎨ 𝑥𝑥 + 5 = 6
⎩ 𝑦𝑦 − 1
9
𝑥𝑥 = 5; 𝑦𝑦 = 4
𝑥𝑥 = 1; 𝑦𝑦 = 2
𝑥𝑥 2
26
+ = 5 − 𝑦𝑦
𝑦𝑦 3
3
⎨𝑥𝑥 + 𝑦𝑦 + 1 = 11
𝑦𝑦 + 1 12
⎩ 2
⎧
𝑥𝑥 = 0; 𝑦𝑦 =
12𝑥𝑥 − 7 5(𝑦𝑦 + 1)
35
+
=
𝑥𝑥 + 2
6
� 2
1
1
8
𝑥𝑥 + 𝑦𝑦 =
5
3
15
𝑥𝑥 + 𝑦𝑦
1
= −
⎧
2
5
5𝑥𝑥
+
3𝑦𝑦
⎨
=0
⎩2𝑥𝑥 + 7𝑦𝑦
25
1
2
𝑥𝑥 = 1; 𝑦𝑦 = 1
𝑥𝑥 = −
𝑥𝑥 =
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18
; 𝑦𝑦 =
13
6
3
; 𝑦𝑦 = −1
5
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Algebra
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v 3.0
Sistemi di equazioni di I grado fratte
𝑥𝑥 − 7
1
+7=
𝑦𝑦
𝑥𝑥
⎨1 + 1 = 𝑥𝑥
⎩𝑥𝑥 𝑦𝑦 + 1 2
⎧
𝑥𝑥 = −1; 𝑦𝑦 = 1
𝑥𝑥 + 𝑦𝑦 − 3
1
=−
⎧
𝑥𝑥 + 𝑦𝑦
2
⎨1 + 3 = 4
⎩ 𝑥𝑥 𝑦𝑦
1
3
; 𝑦𝑦 =
2
2
𝑥𝑥 = 1; 𝑦𝑦 = 1
𝑥𝑥 =
𝑥𝑥 − 1 𝑥𝑥
1
+ =−
𝑦𝑦 + 1 𝑦𝑦
3
⎨5𝑥𝑥 + 7𝑦𝑦 + 𝑦𝑦 = −5
⎩ 𝑥𝑥 − 𝑦𝑦
⎧
𝑥𝑥 = 0; 𝑦𝑦 = 2
3𝑥𝑥
𝑥𝑥 + 𝑦𝑦
9
+
=−
� 𝑦𝑦 − 3 2𝑥𝑥 − 𝑦𝑦
10
−𝑥𝑥 + 2𝑦𝑦 + 7 = 0
𝑥𝑥 = 1; 𝑦𝑦 = −3
91
784
𝑥𝑥 =
; 𝑦𝑦 = −
237
237
𝑥𝑥 =
𝑥𝑥 + 𝑦𝑦 − 5
59
=−
𝑥𝑥 − 𝑦𝑦
4
⎨ 3𝑥𝑥 − 5𝑦𝑦 = 0
⎩6𝑥𝑥 + 10𝑦𝑦 − 1
⎧
𝑥𝑥 =
5𝑥𝑥 − 𝑦𝑦
1
⎧
= 𝑥𝑥 −
11𝑥𝑥 + 7𝑦𝑦
7
⎨ 3𝑥𝑥 − 5𝑦𝑦
= −1
⎩
5
117
133
; 𝑦𝑦 = −
13
7
2
2
; 𝑦𝑦 =
3
5
𝑥𝑥 = 0; 𝑦𝑦 = 1
523
15
; 𝑦𝑦 =
𝑥𝑥 = −
532
532
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