Răspuns:
Explicație pas cu pas:
1a) {2x+3y = 1
{-3x-y = 2 I·3 =>
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{2x+3y = 1
{-9x-3y = 6
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-7x = 7 => x = -1
y = -3x-2 = (-3)·(-1) - 2 = 3-2 => y = 1
1b) {2(x-1)-(x+y) = -3
{3(x-2)+5(x+y) = 9 <=>
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{2x-2-x-y = -3
{3x-6+4x+4y = 9 <=>
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{x-y = -1 I·4 =>
{7x+4y = 15
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{4x-4y = -4
{7x+4y = 15
==========
11x = 11 => x = 1
y = x+1 => y = 2
2a) {³⁾(x+y)/2 + ²⁾(x-y)/3 = ⁶⁾1
{(2x-y+1)/4 = ²⁾(x+y-2)/2 =>
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{3x+3y+2x-2y = 6
{2x-y+1 = 2x+2y-4 <=>
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{5x+y = 6
{3y = 5 => y = 5/3
x = (6-y)/5 = (6-5/3)/5 = > x = 13/15
2b) {(x+1)² = (x+2)(x-3)+y
{(x-2)(y+2) = xy-10 <=>
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{x²+2x+1 = x²-x-6+y
{xy+2x-2y-4 = xy-10 <=>
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{3x-y = -7
{2x-2y = -6 I:(-2) =>
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{3x-y = -7
{-x+y = 3
=======
2x = -4 => x = -2
y = x+3 => y = 1
4) {2ax-b = y+3
{x+2a = 4b+2y
(x ; y) = (1 ; 1) => x = 1 ; y = 1 =>
{2a-b = 4
{2a+1 = 4b+2 <=>
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{2a-b = 4
{2a-4b = 1 I·(-1) =>
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{2a-b = 4
{-2a+4b = -1
=========
3b = 3 => b = 1
2a = b+4 = 5 => a = 5/2
