Question

$5x + y - 11 \\ 2x + 3y = - 7 \\ \\ \\ 3x + y = 6 \\ 2x + 3y = 11$
Rezolvați prin metoda substituției.
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Answer 1

Răspuns:

$\left \{ {{5x+y=-11\:\:|-5x} \atop {2x+3y=-7}} \right. < = > \left \{ {{y=-11-5x} \atop {2x+3y=-7}} \right. < = > \left \{ {{y=-11-5x} \atop {2x+3(-11-5x)=-7}} \right. < = > \left \{ {{y=-11-5x} \atop {2x-33-15x=-7}} \right. < = > \\ < = > \left \{ {{y=-11-5x} \atop {-13x-33=-7\:\:|+33}} \right. < = > \left \{ {{y=-11-5x} \atop {-13x=26\:\:|:(-13)}} \right. < = > \left \{ {{y=-11-5x} \atop {x=-2}} \right. < = > \left \{ {{y=-11-5\times(-2)} \atop {x=-2}} \right. < = > \\ < = > \left \{ {{y=-11+10} \atop {x=-2}} \right.$

$< = > \bf\red{\left \{ {{y=-1} \atop {x=-2}} \right. }$

$\left \{ {{3x+y=6\:\:|-3x} \atop {2x+3y=11}} \right. < = > \left \{ {{y=6-3x} \atop {2x+3y=11}} \right. < = > \left \{ {{y=6-3x} \atop {2x+3(6-3x)=11}} \right. < = > \left \{ {{y=6-3x} \atop {2x+18-9x=11}} \right. < = > \\ < = > \left \{ {{y=6-3x} \atop {-7x+18=11\:\:|-18}} \right. < = > \left \{ {{y=6-3x} \atop {-7x=-7\:\:|:(-7)}} \right. < = > \left \{ {{y=6-3x} \atop {x=1}} \right. < = > \left \{ {{y=6-3\times1} \atop {x=1}} \right. < = > \\ < = > \left \{ {{y=6-3x} \atop {x=1}} \right.$

$\left \{ {y=6-3\times1\atop {x=1}} \right. < = > \bf\red{\left \{ {{y=3} \atop {x=1}} \right. }$