Răspuns:
Explicație pas cu pas:
a)
{ 2 x - y = 3
{ 9 x + y = 19
___________ adun relatiile
11 x = 22 => x = 22 : 11 => x = 2
2 x - y = 3
2 × 2 - y = 3
4 - y = 3
y = 4 - 3 => y = 1
Solutii ( x; y) = ( 2; 1 )
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b)
{ 2 x - 7 y = - 8
{ - 2 x + 9 y = 12
_____________ adun relatiile
/ 2 y = - 8 + 12
2 y = 4 => y = 4 : 2 => y = 2
2 x - 7 y = - 8
2 x - 7 × 2 = - 8
2 x - 14 = - 8
2 x = - 8 + 14
2 x = 6 => x = 6 : 2 => x = 3
Solutii ( x; y) = ( 3; 2)
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c)
{ 4 x - 7 y = 11
{ 6 x + 7 y = - 1
___________ adun relatiile
10 x = 11 + ( - 1 )
10 x = 10 => x = 10 : 10 => x = 1
4 x - 7 y = 11
4 - 7 y = 11
- 7 y = 11 - 4
- 7 y = 7 => y = - 1
Solutii ( x; y) = ( 1; - 1 )
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d)
{ 2 x + 5 y = 0
{ - x - 4 y =3 [ × 2
_________________
{ 2 x + 5 y = 0
{- 2 x - 8 y = 6
____________ adun relatiile
/ - 3 y = 6 => y = - 2
- x - 4 y = 3
- x - 4 × ( - 2 ) = 3
- x + 8 = 3
- x = 3 - 8 => x = 5
Solutii ( x; y ) = ( 5; - 2)
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e)
{ 5 x - y = 6 [ × 3
{ 4 x + 3 y = 1
____________
{ 15 x - 3 y = 18
{ 4 x + 3 y = 1
____________ adun relatiile
19 x = 19 => x = 19 : 19 => x = 1
5 x - y = 6
5 - y = 6
- y = 6 - 5 => y = - 1
Solutii ( x; y) = ( 1; - 1)
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f)
{ x - 2 y = - 2 [ × 2
{ 2 x - 7 y = - 1
____________
{ 2 x - 4 y = - 4
{ 2 x - 7 y = - 1
___________ scad relatiile
/ - 4 y - ( - 7 y ) = - 4 - ( - 1 )
- 4 y + 7 y = - 4 + 1
3 y = - 3 => y = - 1
x - 2 y = - 2
x + 2 = - 2
x = - 2 - 2 => x = - 4
Solutii ( x; y) = ( - 4; - 1 )
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g)
{ 4 x - y = 11 [ × - 5
{ 7 x - 5 y = 16
____________
{ - 20 x + 5 y= - 55
{ 7 x - 5 y = 16
____________ adun relatiile
- 13 x = - 39 => x = 3
4 x - y = 11
12 - y = 11
y = 12 - 11 => y = 1
Solutii ( x; y) = ( 3; 1)
Verific:
4 x - y = 4×3 - 1 = 12 - 1 = 11 √
7 x - 5 y = 7 ×3 - 5 ×1 = 21 - 5 = 16 √
