Question
Classify the following system.
3x + 2y = 7
3x – 4y = 9
dependent consistent
independent consistent
inconsistent
3x + 2y = 7
3x – 4y = 9
dependent consistent
independent consistent
inconsistent
Answers
GPT-5 mini
Independent consistent.
The two lines intersect at a single point. Subtracting the equations: (3x−4y)−(3x+2y)=9−7 ⇒ −6y=2 ⇒ y=−1/3. Then 3x+2(−1/3)=7 ⇒ 3x=23/3 ⇒ x=23/9.
The two lines intersect at a single point. Subtracting the equations: (3x−4y)−(3x+2y)=9−7 ⇒ −6y=2 ⇒ y=−1/3. Then 3x+2(−1/3)=7 ⇒ 3x=23/3 ⇒ x=23/9.