Question

si metoda substitutiei
urgent va rog dau coroana
​

Answer 1

Răspuns:

a) $\left \{ {{3(x+2)+2y=y-5} \atop {2x+2(y-6)=3x-6}} \right.$

$\left \{ {{3x+6+2y=y-5} \atop {2x+2y-12=3x-6}} \right.$

$\left \{ {{3x+y=-11} \atop {-x+2y=6 /*3}} \right.$

$\left \{ {{3x+y=-11} \atop {-3x+6y=18}} \right.$

7y=7 ⇒ y=1  

3x+1=-11   3x=-12   ⇒ x=-4

b) $\left \{ {{3x-2(x+y)=6} \atop {2(x-y) +4y=0}} \right.$

$\left \{ {{3x-2x-2y=6} \atop {2x-2y +4y=0}} \right.$

$\left \{ {{x-2y=6} \atop {2x+2y=0}} \right.$

3x=6  x=3  

3-2y=6  2y=-3  y=$-\frac{3}{2}$

c) $\left \{ {{3(x+3)=2(y+5)} \atop {5(x+1)=4(y+1)}} \right.$

$\left \{ {{3x+9=2y+10} \atop {5x+5=4y+4}} \right.$

$\left \{ {{3x-2y=1/*(-2)} \atop {5x-4y=-1}} \right.$

$\left \{ {{-6x+4y=-2} \atop {5x-4y=-1}} \right.$

-x=-3    x=3

3·3-2y=1  2y=8  y=4  

d) $\left \{ {{6(x-4)+2y=3(y-4)} \atop {4(x+2y)=5(y+6)}} \right.$

$\left \{ {{6x-24+2y=3y-12} \atop {4x+8y=5y+30}} \right.$

$\left \{ {{6x-y=12/*3} \atop {4x+3y=30}} \right.$

$\left \{ {{18x-3y=36} \atop {4x+3y=30}} \right.$

22x=66  x=3

6·3-y=12   y=18-16  y=6

e) $\left \{ {{-3(x+y)-8=y+2} \atop {2(x+4)-2=-3y}} \right.$

$\left \{ {{-3x-3y-8=y+2} \atop {2x+8-2=-3y}} \right.$

$\left \{ {{-3x-4y=10/*2} \atop {2x+3y=-6/*3}} \right.$

$\left \{ {{-6x-8y=20} \atop {6x+9y=-18}} \right.$

y=2  

2x+3·2=-6    2x=-12  x=-6

f) $\left \{ {{5(x-4)+8=9y+10} \atop {4(y+2)+7=3x-1}} \right.$

$\left \{ {{5x-20+8=9y+10} \atop {4y+8+7=3x-1}} \right.$

$\left \{ {{5x-9y=22/*3} \atop {-3x+4y=-16/*5}} \right.$

$\left \{ {{15x-27y=66} \atop {-15x+20y=-80}} \right.$

-7y=-34  y=$\frac{34}{7}$

5x-9· $\frac{34}{7}$=22 /·7   35x-306=154   35x=460  x=$\frac{92}{7}$

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