Question
Identify the pair of linear equations that have the same solution set.(1 point)
Responses
4=k/2+5
and 4j−14/3+5=3
4 equals Start Fraction k over 2 End Fraction plus 5 and Start Fraction 4 j minus 14 over 3 End Fraction plus 5 equals 3
3(m+1)=10
and 6n+3=6−n
3 left parenthesis m plus 1 right parenthesis equals 10 and 6 n plus 3 equals 6 minus n
2(3g+5)−2g=2(4−g)
and −36h/6=2
2 left parenthesis 3 g plus 5 right parenthesis minus 2 g equals 2 left parenthesis 4 minus g right parenthesis and Start Fraction negative 36 h over 6 End Fraction equals 2
4k−5=2k
and 8j−2=3j
Responses
4=k/2+5
and 4j−14/3+5=3
4 equals Start Fraction k over 2 End Fraction plus 5 and Start Fraction 4 j minus 14 over 3 End Fraction plus 5 equals 3
3(m+1)=10
and 6n+3=6−n
3 left parenthesis m plus 1 right parenthesis equals 10 and 6 n plus 3 equals 6 minus n
2(3g+5)−2g=2(4−g)
and −36h/6=2
2 left parenthesis 3 g plus 5 right parenthesis minus 2 g equals 2 left parenthesis 4 minus g right parenthesis and Start Fraction negative 36 h over 6 End Fraction equals 2
4k−5=2k
and 8j−2=3j
Answers
GPT-5 mini
The third pair.
Work:
2(3g+5)−2g = 6g+10−2g = 4g+10. Right side 2(4−g)=8−2g. So 4g+10 = 8−2g ⇒ 6g = −2 ⇒ g = −1/3.
−36h/6 = 2 ⇒ −6h = 2 ⇒ h = −1/3.
Both give −1/3, so they have the same solution set.
Work:
2(3g+5)−2g = 6g+10−2g = 4g+10. Right side 2(4−g)=8−2g. So 4g+10 = 8−2g ⇒ 6g = −2 ⇒ g = −1/3.
−36h/6 = 2 ⇒ −6h = 2 ⇒ h = −1/3.
Both give −1/3, so they have the same solution set.