• # question_answer If the system of equations $2x+3y=7$             $2ax+(a+b)y=28$ has infinitely many solutions, then the values of a and b respectively are ____. A)  2. 5                B)  5, 8                C)  4, 8            D)         3, 6

Given equations are                       $2x+3y=7$and $2ax+(a+b)\,y=28$ For infinitely many solutions, we have                      $\frac{2}{2a}=\frac{3}{a+b}=\frac{7}{28}$ Taking first two members, we get $2a+2b=6a;$ $\Rightarrow$  $4a=2b$      $\Rightarrow$ $2a=b$       .....(1) Also,    $\frac{2}{2a}=\frac{7}{28}$  $\Rightarrow$ $a=4$ From (1) and (2), we have $2(4)=b\,\,\Rightarrow \,\,\,b=8$