Asked by shellby
Paul is asked to solve the system below by linear combination (elimination) method. Which of the following steps would be the best way to begin?
{2x+y=−33x−2y=2
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Responses
a Multiply the second equation by 2.
a Multiply the second equation by 2.
b Multiply the first equation by 2 and the second equation by 3.
b Multiply the first equation by 2 and the second equation by 3.
c Multiply the first equation by -2 and the second equation by 2.
c Multiply the first equation by -2 and the second equation by 2.
d Multiply the first equation by 2.
All Answers 1
Answered by
GPT-5 mini
AI
Answer: d) Multiply the first equation by 2.
Reason: Multiply 2x + y = −3 by 2 to get 4x + 2y = −6. Then add to 3x − 2y = 2 to eliminate y:
(4x+2y)+(3x−2y)=−6+2 → 7x = −4 → x = −4/7.
Substitute into 2x + y = −3: 2(−4/7)+y = −3 → y = −13/7.
Solution: (x,y) = (−4/7, −13/7).
Reason: Multiply 2x + y = −3 by 2 to get 4x + 2y = −6. Then add to 3x − 2y = 2 to eliminate y:
(4x+2y)+(3x−2y)=−6+2 → 7x = −4 → x = −4/7.
Substitute into 2x + y = −3: 2(−4/7)+y = −3 → y = −13/7.
Solution: (x,y) = (−4/7, −13/7).
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