Identify the pair of linear equations that have the same solution set.

Question

(1 point)
3 m+ 1) = 10
and 6n + 3 = 6 - n
4 =
4j-14
and -
3
- + 5 =3
2 3g + 5) - 2g = 2 (4 - g)
-36h
and
= 2
6
4k - 5 = 2k
and 8j - 2 = 3j

Answer 1

To identify the pair of linear equations that have the same solution set, we need to manipulate each equation set to see if they lead to the same linear equation.

1. Equations:

   • $3m+1=10$
   • $6n+3=6-n$

   Solving the first equation: $$3m+1=10⟹3m=9⟹m=3$$

   Solving the second equation: $$6n+3=6-n⟹6n+n=6-3⟹7n=3⟹n=\frac{3}{7}$$ (This pair does not have the same solution set.)

2. Equations:

   • $4=4j-14$
   • $-\frac{3}{2}+5=3$

   Solving the first equation: $$4=4j-14⟹4j=18⟹j=\frac{18}{4}=\frac{9}{2}$$

   Solving the second equation is unclear based on the notation, but assuming it simplifies to a number: $$-\frac{3}{2}+5=\frac{7}{2}⟹(Thisnumberdoesnotrepresentavariable.)$$ (This pair does not have the same solution set.)

3. Equations:

   • $2(3g+5)-2g=2(4-g)$

   Simplifying the equation: $$2(3g+5)-2g=2(4-g)$$ $$6g+10-2g=8-2g⟹4g+10=8-2g⟹6g=-2⟹g=-\frac{1}{3}$$

4. Equations:

   • $-36h=2$
   • $4k-5=2k$

   Solving the first equation: $$-36h=2⟹h=-\frac{1}{18}$$

   Solving the second equation: $$4k-5=2k⟹4k-2k=5⟹2k=5⟹k=\frac{5}{2}$$ (This pair does not have the same solution set.)

5. Equations:

   • $4k-5=2k$
   • $8j-2=3j$

   Solving the first equation (already done as above): $$2k=5⟹k=\frac{5}{2}$$

   Solving the second equation: $$8j-2=3j⟹8j-3j=2⟹5j=2⟹j=\frac{2}{5}$$ (This pair does not have the same solution set.)

Now, from the pairs we have evaluated, we have not found two pairs that yield the same solution set.

Therefore, there is no pair among the given equations that have the same solution set based on our analysis.

If there is a specific suggestion or insight on how you would like me to approach further or clarify, please let me know!