Răspuns:
Explicație pas cu pas:
Sistem: Folosesc metoda substitutiei
{ x - 2 y = 1 => x = 1 + 2 y
{ 2 x - y = 7
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2 x - y = 7
2(1+2y) - y = 7
2 + 4 y - y = 7
3 y = 7 - 2
y = 5/3
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x = 1 + 2 × 5/3 => x = (3+10)/3 => x = 13/3
Solutii ( x; y) = ( 13/3; 5/3)
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Verific:
x - 2 y = 13/3 - 2×5/3 = 3/3 = 1
2 x - y = 2 ×13/3 - 5/3 = 21/3 = 7
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Daca ai postat gresit sistemul, eu l-am rezolvat in forma postata de tine!
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- Am vazut in comentarii forma corecta a sistemului si postez si solutia acestui sistem
{ x - 2 y = - 1 => x = 2 y - 1
{ 2 x - y = 7
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Inlocuiesc in a doua relatie pe x:
2 x - y = 7
2 ( 2 y - 1 ) - y = 7
4 y - 2 - y = 7
4 y - y = 7 + 2
3 y = 9
y = 9 : 3 => y = 3
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x = 2 y - 1 = 2 × 3 - 1 = 6 - 1 => x = 5
Solutia ( x; y ) = ( 5; 3)
Verific:
{ x - 2 y = 5 - 2 × 3 = 5 - 6 = - 1
{ 2 x - y = 2 × 5 - 3 = 10 - 3 = 7
