DivyaD wrote:Does (a – 2)(b + 4) = 8?
(1) ab = 2b – 4a
(2) a = 6
$$\left( {a - 2} \right)\left( {b + 4} \right)\,\,\mathop = \limits^? \,\,8$$
$$\left( 1 \right)\,\,ab = 2b - 4a\,\,\,\,\mathop \Rightarrow \limits^{{\rm{focus}}!} \,\,\,\,a\left( {b + 4} \right) = 2b\,\,\,\,\mathop \Rightarrow \limits^{{\rm{focus}}!} \,\,\,\,\left( {a - \underline 2 } \right)\left( {b + 4} \right) + \underline {2\left( {b + 4} \right)} = 2b$$
$$\,\,\,\,\mathop \Rightarrow \limits^{{\rm{focus}}!} \,\,\,\,\left( {a - 2} \right)\left( {b + 4} \right) = 2b - 2\left( {b + 4} \right) = - 8 \ne 8\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,a = 6\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {6, - 4} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {6, - 2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
