19. Rezolvați prin metoda reducerii următoarele sisteme:
Va rog repede
Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
a) {³⁾(x+3)/4 = ²⁾(y+5)/6
{⁹⁾(x-7)/2 = ²⁾(5-2y)/9 <=>
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{3x+9 = 2y+10
{9x-63 = 10-4y <=>
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{3x-2y = 1 I·2
{9x+4y = 73 =>
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{6x-4y = 2
{9x+4y = 73 =>
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15x = 75 => x = 75/15 => x = 5
3·5-2y = 1 => 2y = 14 => y = 7
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b) {(2x+y-1)/(4x+2y)=1/4
{(3x+2y-5)/(3x+y-1) = 3/7 <=>
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{8x+4y-4 = 4x+2y
{21x+14y-35 = 9x+3y-3 <=>
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{4x+2y = 4 I·3
{12x+11y = 32 =>
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{12x+6y = 12
{12x+11y = 32 =>
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5y = 20 => y = 4
4x+8= 4 => 4x = -4 => x = -1
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c) {(x+4)/2 + ²⁾y = ²⁾7
{(y-2)/2 + ²⁾x = ²⁾3 <=>
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{x+4+2y = 14
{y-2+2x = 6 <=>
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{x+2y = 10
{2x+y = 8 I·2 =>
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{x+2y = 10
{4x+2y = 16
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3x = 6 => x = 2
2+2y = 10 => 2y = 8 => y = 4
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d) {(x+2)/3 = ³⁾-3-³⁾y
{²⁾x + (y-2)/2 = ²⁾-2 <=>
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{x+2 = -9-3y
{2x+y-2 = -4 <=>
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{x+3y = -11
{2x+y = -2 I·3 =>
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{x+3y = -11
{6x+3y = -6
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5x = -6+11 = 5 => x = 1
1+3y = -11 => 3y = -12 => y = -4