Question

Rezolvati prin metoda substitutiei 4x-3y=13 2(x-y)+5y=-7 5(x+2)-3=y x+2(y+1)=5

Answer 1

Bună!

a) $\left \{ {{4x-3y=13} \atop {2(x-y)+5y=-7}} \right. => \left \{ {{y=-\frac{13}{3}+\frac{4x}{3} } \atop {2(x-y)+5y=-7}} \right. => 2[x-(-\frac{13}{3}+\frac{4x}{3} )]+5(-\frac{13}{3} +\frac{4x}{3} )=-7$

$<=> 2(^{3)} x+\frac{13}{3} -\frac{4x}{3} )-\frac{65}{3} +\frac{20x}{3} <=>$

$<=> 2(-\frac{x}{3} +\frac{13}{3} )-\frac{65}{3} +\frac{20x}{3} =-7 <=>$

$<=> -\frac{2x}{3} +\frac{26}{3} -\frac{65}{3} +\frac{20x}{3} =-7 <=>$

$<=> 6x-13=-7/+13 => 6x=6 => x=1$

$y=-\frac{13}{3} +\frac{4}{3} =-\frac{9}{3}=> y=-3$

b) $\left \{ {{5(x+2)-3=y} \atop {x+2(y+1)=5}} \right. => \left \{ {{5x+10-3=y} \atop {x+2y+2=5}} \right. => \left \{ {{5x+7=y} \atop {x+2y=3}} \right. =>$

$=> x+2(5x+7)=3 => x+10x+14=3 => 11x=-11 => x=-1$

$y=5*(-1)+7=-5+7=> y=2$

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