To determine which ordered pair is a solution to the equation [tex]\( y = 7x - 3 \)[/tex], we need to test each pair by substituting [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values into the equation and checking for equality.
Let's go through each ordered pair one by one:
1. Ordered pair [tex]\( F(-2, -17) \)[/tex]:
- Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
y = 7(-2) - 3
\][/tex]
Simplify the expression:
[tex]\[
y = -14 - 3 = -17
\][/tex]
- Since [tex]\( y = -17 \)[/tex] matches the value in the pair, [tex]\( F(-2, -17) \)[/tex] is indeed a solution to the equation.
2. Ordered pair [tex]\( H(2, 7) \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
y = 7(2) - 3
\][/tex]
Simplify the expression:
[tex]\[
y = 14 - 3 = 11
\][/tex]
- Since [tex]\( y = 11 \)[/tex] does not match the value in the pair [tex]\( H(2, 7) \)[/tex], this pair is not a solution.
3. Ordered pair [tex]\( G(-2, 11) \)[/tex]:
- Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
y = 7(-2) - 3
\][/tex]
Simplify the expression:
[tex]\[
y = -14 - 3 = -17
\][/tex]
- Since [tex]\( y = -17 \)[/tex] does not match the value in the pair [tex]\( G(-2, 11) \)[/tex], this pair is not a solution.
4. Ordered pair [tex]\( I(2, 14) \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
y = 7(2) - 3
\][/tex]
Simplify the expression:
[tex]\[
y = 14 - 3 = 11
\][/tex]
- Since [tex]\( y = 11 \)[/tex] does not match the value in the pair [tex]\( I(2, 14) \)[/tex], this pair is not a solution.
Therefore, the only ordered pair that is a solution to the equation [tex]\( y = 7x - 3 \)[/tex] is [tex]\( F(-2, -17) \)[/tex].
