1.
а) {3a+7b =8 ;a+5b =4. ⇔{3(4-5b) +7b=8 ; a =4-5b. ⇔{b=0,5 ; a=1,5.
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б) {2(2x-y) +3(2x+y) =32 ;5(2x-y) -2(2x+y) =4 ⇔
{4(2x-y) +6(2x+y) =64 ; 15(2x-y) -6(2x+y) =12⇔|| +||
{19(2x-y) =76 ; 15(2x-y) -6(2x+y) =12 ⇔{ 2x-y =4 ; 2x+y =8 || ±||
{ x=3 ; y=2 .
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2. {3(x+y) +5(x-y) =92 ;5(x+y) -6(x-y) =10.⇔{4x -y =46 ; -x +11y =10 ⇔
{4x -y =46 ; -4x +44y =40 ⇔{4x -y =46 ;43y =86 ⇔{x =12 ; y =2 .
* * *или замена x+y =u , x-y =v ⇒{3u +5v =92 ;5u -6v =10 * * *
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3. y =kx +b ⇒{ 2k+b= -1 ; -2k +b = -3. || ±|| { k = 1/2 ; b=-2.
ответ: y =(1/2)x - 2.
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4. Решить уравнение :
|x-y-3| +x² -4xy +4y² =0 ⇔ |x-y-3| +(x -2y)² =0 ⇔{ x-y -3=0 ; x-2y=0 ⇔
{ 2y-y =3 ; x=2y.⇔{ y =3 ; x=6.
ответ: x=6 , y =3 .