Vì hpt có nghiệm (3; 2) nên ta có: x = 3; y = 2
Thay x = 3; y = 2 vào hpt, ta có:
$\left \{ {{3a+2y=6} \atop {2.3.a-3.2.b = 72}} \right.$
⇔ $\left \{ {{3a+2b=6} \atop {6a-6b = 72}} \right.$
⇔ $\left \{ {{3a=6-2b} \atop {6a-6b = 72}} \right.$
⇔ $\left \{ {{a=\frac{6-2b}{3} } \atop {6(\frac{6-2b}{3})-6b = 72}} \right.$
⇔ $\left \{ {{a=\frac{6-2b}{3} } \atop {\frac{36-12b}{3}-6b = 72}} \right.$
⇔ $\left \{ {{a=\frac{6-2b}{3} } \atop {\frac{36-12b}{3}-\frac{18b}{3}= \frac{216}{3} }} \right.$
⇔ $\left \{ {{a=\frac{6-2b}{3} } \atop {36-12b-18b= 216 }} \right.$
⇔ $\left \{ {{a=\frac{6-2b}{3} } \atop {-30b= 216 - 36}} \right.$
⇔ $\left \{ {{a=\frac{6-2b}{3} } \atop {-30b= 180}} \right.$
⇔ $\left \{ {{a=\frac{6-2b}{3} } \atop {b= -6}} \right.$
⇔ $\left \{ {{a=\frac{6-2(-6)}{3} } \atop {b= -6}} \right.$
⇔ $\left \{ {{a=\frac{18}{3} } \atop {b= -6}} \right.$
⇔ $\left \{ {{a=6} \atop {b= -6}} \right.$
Vậy a = 6; b = -6 thì hpt $\left \{ {{3a+2y=6} \atop {2.3.a-3.2.b = 72}} \right.$ có nghiệm (3; 2).
