Answer :
To determine which ordered pair is a solution to the equation [tex]\( y - 3 = 5(x - 2) \)[/tex], let's substitute each pair into the equation and see if it holds true.
### First Pair: [tex]\((2, 3)\)[/tex]
1. Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex] into [tex]\( y - 3 = 5(x - 2) \)[/tex]:
[tex]\[ 3 - 3 = 5(2 - 2) \][/tex]
2. Simplify the left side and right side of the equation:
[tex]\[ 0 = 5(0) \][/tex]
[tex]\[ 0 = 0 \][/tex]
Since the equation holds true, the ordered pair [tex]\((2, 3)\)[/tex] satisfies the equation.
### Second Pair: [tex]\((3, 2)\)[/tex]
1. Substitute [tex]\(x = 3\)[/tex] and [tex]\(y = 2\)[/tex] into [tex]\( y - 3 = 5(x - 2) \)[/tex]:
[tex]\[ 2 - 3 = 5(3 - 2) \][/tex]
2. Simplify the left side and right side of the equation:
[tex]\[ -1 = 5(1) \][/tex]
[tex]\[ -1 = 5 \][/tex]
Since the equation does not hold true, the ordered pair [tex]\((3, 2)\)[/tex] does not satisfy the equation.
### Conclusion
From the above analysis, we can see that only [tex]\((2, 3)\)[/tex] satisfies the given equation.
Thus, the correct answer is:
(A) Only [tex]\((2, 3)\)[/tex]
### First Pair: [tex]\((2, 3)\)[/tex]
1. Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex] into [tex]\( y - 3 = 5(x - 2) \)[/tex]:
[tex]\[ 3 - 3 = 5(2 - 2) \][/tex]
2. Simplify the left side and right side of the equation:
[tex]\[ 0 = 5(0) \][/tex]
[tex]\[ 0 = 0 \][/tex]
Since the equation holds true, the ordered pair [tex]\((2, 3)\)[/tex] satisfies the equation.
### Second Pair: [tex]\((3, 2)\)[/tex]
1. Substitute [tex]\(x = 3\)[/tex] and [tex]\(y = 2\)[/tex] into [tex]\( y - 3 = 5(x - 2) \)[/tex]:
[tex]\[ 2 - 3 = 5(3 - 2) \][/tex]
2. Simplify the left side and right side of the equation:
[tex]\[ -1 = 5(1) \][/tex]
[tex]\[ -1 = 5 \][/tex]
Since the equation does not hold true, the ordered pair [tex]\((3, 2)\)[/tex] does not satisfy the equation.
### Conclusion
From the above analysis, we can see that only [tex]\((2, 3)\)[/tex] satisfies the given equation.
Thus, the correct answer is:
(A) Only [tex]\((2, 3)\)[/tex]
