Question

daca se mareste un numar de 5 ori si altul de 9 ori suma lor devine 408. daca se mareste primul numar de 10 ori si al doilea de 6 ori suma lor devine 432. afla cele doua numere

Answer 1

5a+9b=408
10a+6b=432
15a+15b=840
15(a+b)=840  => a+b=840:15  => a+b=56  => a=56-b
5(56-b)+9b=408 
280-5b+9b=408
4b=408-280  => 4b=128  => b=128:4  => b=32
a=56-b  => a=56-32  => a=24
Verificam:  5x24+9x32= 120+288= 408
                  10x24+6x32= 240+192= 432

Answer 2

$\left \{ {{5x+9y=408} \atop {10x+6y=432}} \right.$⇔$\left \{ {{10x+18y=816} \atop 10{x+6y=432}} \right. \\ \left \{ {{12y=384} \atop {10x=432-6y}} \right. \\ \left \{ {{y=32} \atop {10x=432-192}} \right. \\ \left \{ {{y=32} \atop {x=24}} \right.$
Raspuns:x=24;y=32