Question

rezolvati prin metoda substitutiei sistemele
{4(x-1)-5y=-18
{3(x+1)-4y=8​

Answer 1

Răspuns:

Explicație pas cu pas:

4x-4-5y=-18

3x+3-4y=8

4x-5y=-14  y=1/5*(4x+14)

3x-4y=5

3x-4*1/5*( 4x+14)=5

x=-81

y=-62

Answer 2

$\displaystyle \left \{ {{4(x-1)-5y=-18} \atop {3(x+1)-4y=8}} \right. \Rightarrow \left \{ {{4x-4-5y=-18} \atop {3x+3-4y=8}} \right. \Rightarrow \left \{ {{4x-5y=-18+4} \atop {3x-4y=8-3}} \right. \Rightarrow \\\\\\ \Rightarrow \left \{ {{4x-5y=-14} \atop {3x-4y=5}} \right. \Rightarrow \left \{ {{x=\cfrac{-14+5y}{4} } \atop {3x-4y=5}} \right. \Rightarrow \left \{ {{x=\cfrac{-14+5y}{4} } \atop {3 \cdot \cfrac{-14+5y}{4} -4y}=5} \right. \Rightarrow$

$\displaystyle \Rightarrow \left \{ {{x=\cfrac{-14+5y}{4}} \atop {-42+15y-16y}=20} \right. \Rightarrow \left \{ {x=\cfrac{-14+5y}{4}} \atop {-y=20+42}} \right. \Rightarrow \left \{ {{x=\cfrac{-14+5y}{4}} \atop {y=-62}} \right. \Rightarrow \\\\\\ \Rightarrow \left \{ {{x=\cfrac{-14+5\cdot (-62)}{4}} \atop {y=-62}} \right. \Rightarrow \left \{ {{x=\cfrac{-14-310}{4} } \atop {y=-62}} \right. \Rightarrow \left \{ {{x=\cfrac{-324}{4} } \atop {y=-62}} \right. \Rightarrow$

                                                                                              $\displaystyle \Rightarrow \left \{ {{x=-81} \atop {y=-62}}$