To determine which ordered pair is a solution to the equation [tex]\( 7x - 5 = 4y - 6 \)[/tex], we need to check both pairs [tex]\((2, 4)\)[/tex] and [tex]\((3, 6)\)[/tex] by substituting these values into the equation and verifying if the equation holds true for each pair.
### Check the ordered pair [tex]\((2, 4)\)[/tex]
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 4 \)[/tex] into the equation [tex]\( 7x - 5 = 4y - 6 \)[/tex]:
1. Calculate [tex]\( 7x - 5 \)[/tex]:
[tex]\[
7(2) - 5 = 14 - 5 = 9
\][/tex]
2. Calculate [tex]\( 4y - 6 \)[/tex]:
[tex]\[
4(4) - 6 = 16 - 6 = 10
\][/tex]
3. Compare the two results:
[tex]\[
9 \neq 10
\][/tex]
Thus, the ordered pair [tex]\((2, 4)\)[/tex] is not a solution to the equation because both sides of the equation are not equal when these values are substituted.
### Check the ordered pair [tex]\((3, 6)\)[/tex]
Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 6 \)[/tex] into the equation [tex]\( 7x - 5 = 4y - 6 \)[/tex]:
1. Calculate [tex]\( 7x - 5 \)[/tex]:
[tex]\[
7(3) - 5 = 21 - 5 = 16
\][/tex]
2. Calculate [tex]\( 4y - 6 \)[/tex]:
[tex]\[
4(6) - 6 = 24 - 6 = 18
\][/tex]
3. Compare the two results:
[tex]\[
16 \neq 18
\][/tex]
Thus, the ordered pair [tex]\((3, 6)\)[/tex] is not a solution to the equation because both sides of the equation are not equal when these values are substituted.
### Conclusion
Since neither [tex]\((2, 4)\)[/tex] nor [tex]\((3, 6)\)[/tex] satisfies the equation [tex]\( 7x - 5 = 4y - 6 \)[/tex],
The correct answer is:
(D) Neither
