MATH SOLVE

3 months ago

Q:
# If a+b=6, b+c=β3, and a+c=5, what is the value of a+b+c?

Accepted Solution

A:

[tex]\bf \begin{cases} a+b=6\\ \boxed{b}=6-a\\[-0.5em] \hrulefill\\ b+c=-3\\ \boxed{6-a}+c=-3\\ -a+c=-9\\ c=-9+a \end{cases}~\hspace{5em} \begin{array}{llll} a+c=5\\\\ \stackrel{\textit{we know that c = -9+a}}{a+(-9+a)=5}\\\\ 2a-9=5\\\\ 2a=14\\\\ a=\cfrac{14}{2}\\\\ \blacktriangleright a=7 \blacktriangleleft \end{array} \\\\[-0.35em] ~\dotfill[/tex][tex]\bf \boxed{b}=6-a\implies b=6-7\implies \blacktriangleright b=-1\blacktriangleleft \\\\\\ c=-9+a\implies c=-9+7\implies \blacktriangleright c=-2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ a+b+c\implies (7)+(-1)+(-2)\implies 4[/tex]