Question

1.Determinati in fiecare caz numarul c stiind ca
a a+b=-6 si a*c+b*c=42
b a+b=-9 si a*c+b*c=-72
c a-b=4 si a*c-b*c=-44
d a-b=-25 si a*c-b*c=-250
2. Calculati a+b stiind ca :
a. a*c+b*c=128 si c=-32
b. a*c+b*c=-96 si c=-3
c.a*c+b*c=-882 si c=-9

Answer 1

$\displaystyle 1a).a+b=-6 \\ a \cdot c+b \cdot c=42 \\ c \cdot (a+b)=42 \\ -6c=42 \\ c=- \frac{42}{6} \\ c=-7 \\ b).a+b=-9 \\ a \cdot c+ b \cdot c=-72 \\ c \cdot (a+b)=-72 \\ -9c=-72 \\ c= \frac{-72}{-9} \\ c=8$
$\displaystyle c).a-b=4 \\ a \cdot c-b \cdot c=-44 \\ c \cdot (a-b)=-44 \\ 4c=-44 \\ c=- \frac{44}{4} \\ c=-11 \\ d).a-b=-25 \\ a \cdot c-b \cdot c=-250 \\ c \cdot (a-b)=-250 \\ -25c=-250 \\ c= \frac{-250}{-25} \\ c= 10$
$\displaystyle 2a).c=-32 \\ a \cdot c+b \cdot c=128 \\ c \cdot (a+b)=128 \\ -32\cdot (a+b)=128 \\ a+b=- \frac{128}{32} \\ a+b=-4 \\ b).c=-3 \\ a \cdot c+b \cdot c=-96 \\ c \cdot (a+b)=-96 \\ -3 \cdot (a+b)=-96 \\ a+b= \frac{-96}{-3} \\ a+b=32$
$\displaystyle c).c=-9 \\ a \cdot c +b \cdot c=-882 \\ c \cdot (a+b)=-882 \\ -9 \cdot (a+b)=-882 \\ a+b= \frac{-882}{-9} \\ a+b=98$