Question

Daca A+B=20 si B+C=30, calculati 3×A+7×B+4×C=
Daca A+B=33 si A+C=11, calculati 5×A+3×B+2×C=
Stiind ca X+3×Y=2×Y+Z=14, calculati:
a) X+5×Y+Z= b)3×X+15×Y+3×Z= c) 5×X+11×Y-2×Z= d) 5×X+19×Y+2×Z=

Answer 1

A+B=20  *3   3A+3B=60  +
B+C=30  *4    4B+4C=120
                     _________
                     3A+7B+4C=180
A+B=33 *3  3A+3B=99 +
A+C=11 *2  2A+2C=22
                 __________
               3A+5B+2C=121

Answer 2

A + B = 20 , B + C = 30 , 3A + 7B + 4C = 3A + 3B + 4B + 4C = 3(A + B) + 4(B + C) = 3 · 20 + 4 · 30 = 180.

A + B = 33 , A + C = 11 , 5A + 3B + 2C = 3A + 2A + 2B + B + 2C = 3A + 3B +
+ 2A + 2C = 3(A + B) + 2(A + C) = 3 · 33 + 2 · 11 = 121

X + 3Y = 2Y + Z = 14 , a) X + 5Y + Z = X + 3Y + 2Y + Z = 14 + 14 = 28 ,
b) 3X + 15Y + 3Z = 3(X + 5Y + Z) = 3 · 28 = 84 (folosesc relatia de deasupra)
c) 5X + 11Y - 2Z = 5X + 15Y - 4Y - 2Z = 5(X + 3Y) - 2(2Y + Z) = 5 · 14 - 2 · 14 =
= 70 - 28 = 42
d) 5X + 19Y + 2Z = 5X + 15Y + 4Y + 2Z = 5(X + 3Y) + 2(2Y + Z) = 5 · 14 + 2 · 14 =
= 70 + 28 = 98