Bonsoir,
Exercice 1 :
(S₁) : [tex]\left \{ {{x-1=0} \atop {y=x+4}} \right. \left \{ {{x=0+1} \atop {y=x+4}} \right. \left \{ {{x=1} \atop {y=1+4}} \right. \left \{ {{x=1} \atop {y=5}} \right.[/tex]
(S₂) : [tex]\left \{ {{2x-3=0} \atop {x+y=1}} \right. \left \{ {{2x=0+3} \atop {x+y=1}} \right. \left \{ {{2x=3} \atop {x+y=1}} \right. \left \{ {{x=\frac{3}{2} } \atop {x+y=1}} \right. \left \{ {{x=1,5} \atop {2,5+y=1}} \right. \left \{ {{x=1,5} \atop {y=1-2,5}} \right. \left \{ {{x=1,5} \atop {y=-1,5}} \right.[/tex]
Exercice 2 :
(S₁) : [tex]\left \{ {{y=4x-\frac{1}{5} } \atop {x=\frac{1}{3} }} \right. \left \{ {{y=\frac{4}{3}-\frac{1}{5} } \atop {x=\frac{1}{3} }} \right. \left \{ {{y=\frac{20}{15} - \frac{4}{15} } \atop {x=\frac{1}{3} }} \left \{ {{y=\frac{16}{15} } \atop {x=\frac{1}{3} }} \right.[/tex]
(S₂) : [tex]\left \{ {{2x + y=\frac{3}{4} } \atop {y=\frac{1}{2} }} \right. \left \{ {{2x + \frac{1}{2} =\frac{3}{4} } \atop {y=\frac{1}{2} }} \right. \left \{ {{2x =\frac{3}{4} - \frac{1}{2} } \atop {y=\frac{1}{2} }} \right. \left \{ {{2x =\frac{3}{4} - \frac{2}{4} } \atop {y=\frac{1}{2} }} \right. \left \{ {{2x =\frac{1}{4} } \atop {y=\frac{1}{2} }} \right. \left \{ {{x =\frac{0,25}{2} } \atop {y=\frac{1}{2} }} \right. \left \{ {{x =0,125 } \atop {y=\frac{1}{2} }} \right.[/tex]
Exercice 3 :
(S₁) :[tex]\left \{ {{x+y=9} \atop {2x-y=3}} \right. \left \{ {{x=9-y} \atop {2(9-y) - y = 3}} \right. \left \{ {{x=9-y} \atop {18 - 10y = 3}} \right. \left \{ {{x=9-y} \atop {10y = 3-18}} \right. \left \{ {{x=9-y} \atop {10y = -15}} \right. \left \{ {{x=9-y} \atop {y = -1,5}} \right. \left \{ {{x=9-(-1,5)} \atop {y = -1,5}} \right. \left \{ {{x=9+1,5)} \atop {y = -1,5}} \right. \left \{ {{x=10,5} \atop {y = -1,5}} \right.[/tex]
(S₂) : [tex]\left \{ {{-x+y=4} \atop {x+3y=5}} \right. \left \{ {{y=4+x} \atop {x+3(4+x)=5}} \right. \left \{ {{y=4+x} \atop {12 + 4x=5}} \right. \left \{ {{y=4+x} \atop {4x=-7}} \right. \left \{ {{y=4+x} \atop {x=-1,75}} \right. \left \{ {{y=4-1,75} \atop {x=-1,75}} \right. \left \{ {{y=2,25} \atop {x=-1,75}} \right.[/tex]
Exercice 4 :
(S₁) : [tex]\left \{ {3x + y = 2} \atop {2x + 3y =5}} \right. \left \{ {y = 2-3x} \atop {2x + 3(2-3x) =5}} \right. \left \{ {y = 2-3x} \atop {6 - 7x =5}} \right. \left \{ {y = 2-3x} \atop {- 7x =-1}} \right. \left \{ {y = 2-3x} \atop {x =\frac{1}{7} }} \right. \left \{ {y = 2-\frac{3}{7} } \atop {x =\frac{1}{7} }} \right. \left \{ {y = \frac{11}{7} } \atop {x =\frac{1}{7} }} \right.[/tex]
(S₂) :[tex]\left \{ {{x-2y=7} \atop {3x + y=1}} \right. \left \{ {{x-2y=7} \atop {y=1-3x}} \right. \left \{ {{x-2(1-3x)=7} \atop {y=1-3x}} \right. \left \{ {{-2 +7x=7} \atop {y=1-3x}} \right. \left \{ {{7x=9} \atop {y=1-3x}} \right. \left \{ {{x=\frac{9}{7} } \atop {y=1-3x}} \right. \left \{ {{x=\frac{9}{7} } \atop {y=1-\frac{27}{7} }} \right. \left \{ {{x=\frac{9}{7} } \atop {y=\frac{-20}{7} }} \right.[/tex]
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Bonsoir,
Exercice 1 :
(S₁) : [tex]\left \{ {{x-1=0} \atop {y=x+4}} \right. \left \{ {{x=0+1} \atop {y=x+4}} \right. \left \{ {{x=1} \atop {y=1+4}} \right. \left \{ {{x=1} \atop {y=5}} \right.[/tex]
(S₂) : [tex]\left \{ {{2x-3=0} \atop {x+y=1}} \right. \left \{ {{2x=0+3} \atop {x+y=1}} \right. \left \{ {{2x=3} \atop {x+y=1}} \right. \left \{ {{x=\frac{3}{2} } \atop {x+y=1}} \right. \left \{ {{x=1,5} \atop {2,5+y=1}} \right. \left \{ {{x=1,5} \atop {y=1-2,5}} \right. \left \{ {{x=1,5} \atop {y=-1,5}} \right.[/tex]
Exercice 2 :
(S₁) : [tex]\left \{ {{y=4x-\frac{1}{5} } \atop {x=\frac{1}{3} }} \right. \left \{ {{y=\frac{4}{3}-\frac{1}{5} } \atop {x=\frac{1}{3} }} \right. \left \{ {{y=\frac{20}{15} - \frac{4}{15} } \atop {x=\frac{1}{3} }} \left \{ {{y=\frac{16}{15} } \atop {x=\frac{1}{3} }} \right.[/tex]
(S₂) : [tex]\left \{ {{2x + y=\frac{3}{4} } \atop {y=\frac{1}{2} }} \right. \left \{ {{2x + \frac{1}{2} =\frac{3}{4} } \atop {y=\frac{1}{2} }} \right. \left \{ {{2x =\frac{3}{4} - \frac{1}{2} } \atop {y=\frac{1}{2} }} \right. \left \{ {{2x =\frac{3}{4} - \frac{2}{4} } \atop {y=\frac{1}{2} }} \right. \left \{ {{2x =\frac{1}{4} } \atop {y=\frac{1}{2} }} \right. \left \{ {{x =\frac{0,25}{2} } \atop {y=\frac{1}{2} }} \right. \left \{ {{x =0,125 } \atop {y=\frac{1}{2} }} \right.[/tex]
Exercice 3 :
(S₁) :[tex]\left \{ {{x+y=9} \atop {2x-y=3}} \right. \left \{ {{x=9-y} \atop {2(9-y) - y = 3}} \right. \left \{ {{x=9-y} \atop {18 - 10y = 3}} \right. \left \{ {{x=9-y} \atop {10y = 3-18}} \right. \left \{ {{x=9-y} \atop {10y = -15}} \right. \left \{ {{x=9-y} \atop {y = -1,5}} \right. \left \{ {{x=9-(-1,5)} \atop {y = -1,5}} \right. \left \{ {{x=9+1,5)} \atop {y = -1,5}} \right. \left \{ {{x=10,5} \atop {y = -1,5}} \right.[/tex]
(S₂) : [tex]\left \{ {{-x+y=4} \atop {x+3y=5}} \right. \left \{ {{y=4+x} \atop {x+3(4+x)=5}} \right. \left \{ {{y=4+x} \atop {12 + 4x=5}} \right. \left \{ {{y=4+x} \atop {4x=-7}} \right. \left \{ {{y=4+x} \atop {x=-1,75}} \right. \left \{ {{y=4-1,75} \atop {x=-1,75}} \right. \left \{ {{y=2,25} \atop {x=-1,75}} \right.[/tex]
Exercice 4 :
(S₁) : [tex]\left \{ {3x + y = 2} \atop {2x + 3y =5}} \right. \left \{ {y = 2-3x} \atop {2x + 3(2-3x) =5}} \right. \left \{ {y = 2-3x} \atop {6 - 7x =5}} \right. \left \{ {y = 2-3x} \atop {- 7x =-1}} \right. \left \{ {y = 2-3x} \atop {x =\frac{1}{7} }} \right. \left \{ {y = 2-\frac{3}{7} } \atop {x =\frac{1}{7} }} \right. \left \{ {y = \frac{11}{7} } \atop {x =\frac{1}{7} }} \right.[/tex]
(S₂) :[tex]\left \{ {{x-2y=7} \atop {3x + y=1}} \right. \left \{ {{x-2y=7} \atop {y=1-3x}} \right. \left \{ {{x-2(1-3x)=7} \atop {y=1-3x}} \right. \left \{ {{-2 +7x=7} \atop {y=1-3x}} \right. \left \{ {{7x=9} \atop {y=1-3x}} \right. \left \{ {{x=\frac{9}{7} } \atop {y=1-3x}} \right. \left \{ {{x=\frac{9}{7} } \atop {y=1-\frac{27}{7} }} \right. \left \{ {{x=\frac{9}{7} } \atop {y=\frac{-20}{7} }} \right.[/tex]