18)
a)
x+y = 123
y+z = 257
5x+7y+2z = 5x+5y+2y+2z = 5(x+y)+2(y+z) = 5·123+2·257 =
= 1129
b)
2a+6b+14 = 152
ax+3bx+7x = 380
x·(a+3b+7) = 380 |·2
2x·(a+3b+7) = 760
x·2(a+3b+7) = 760
x·(2a+6b+14) = 760
x·152 = 760
x = 760:152
x = 5
La exercitiul 17 d)
[tex]60x-x-2x-3x-...-10x\leq 49-2x \\ \\ 60x-x\cdot (1+2+3+...+10)\leq 49-2x \\ \\ 60x-x\cdot \dfrac{10\cdot (10+1)}{2}\leq 49-2x\\ \\ 60x-x\cdot \dfrac{10\cdot 11}{2}\leq 49-2x\\ \\ 60x-x\cdot 5\cdot 11\leq 49-2x \\ \\ 60x-55x\leq 49-2x \\ \\ 5x\leq 49-2x \\ \\ 5x+2x\leq49 \\ \\ 7x\leq 49 \\ \\ x\leq \dfrac{49}{7} \\ \\ x\leq 7\\ \\$ $ S= \Big\{0,1,2,3,4,5,6,7\Big\}[/tex]
