BTGmoderatorDC wrote:If 3x + 2y = -2z, what is x?
(1) x - y - z = 10
(2) x + y + z = -2
\[? = x\]
\[3x + 2y = - 2z\,\,\,\, \Rightarrow \,\,\,\,3x = - 2\left( {y + z} \right)\,\,\,\,\,\,\left( * \right)\]
\[\left( 1 \right)\,\,\,\,x - \left( {y + z} \right) = 10\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,\,\,\,2x - 2\left( {y + z} \right) = 20\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,2x + 3x = 20\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x\,\,\,{\text{unique}}\]
\[\left( 2 \right)\,\,\,x + \left( {y + z} \right) = - 2\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,\,\,\,2x + 2\left( {y + z} \right) = - 4\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,2x - 3x = - 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x\,\,\,{\text{unique}}\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
