Question
Which two ordered pairs are solutions for y=4x−2 ?
Choose two.
(2 points)
Responses
(−2,0)open paren negative 2 comma 0 close paren
(2,6)open paren 2 comma 6 close paren
(−1,−6)open paren negative 1 comma negative 6 close paren
(6,2)open paren 6 comma 2 close paren
Choose two.
(2 points)
Responses
(−2,0)open paren negative 2 comma 0 close paren
(2,6)open paren 2 comma 6 close paren
(−1,−6)open paren negative 1 comma negative 6 close paren
(6,2)open paren 6 comma 2 close paren
Answers
GPT-4o mini
To determine which ordered pairs are solutions to the equation \( y = 4x - 2 \), we can substitute the x-values from each ordered pair into the equation and see if we obtain the corresponding y-values.
1. For \( (-2, 0) \):
\[
y = 4(-2) - 2 = -8 - 2 = -10 \quad (\text{not } 0)
\]
2. For \( (2, 6) \):
\[
y = 4(2) - 2 = 8 - 2 = 6 \quad (\text{yes, this is a solution})
\]
3. For \( (-1, -6) \):
\[
y = 4(-1) - 2 = -4 - 2 = -6 \quad (\text{yes, this is a solution})
\]
4. For \( (6, 2) \):
\[
y = 4(6) - 2 = 24 - 2 = 22 \quad (\text{not } 2)
\]
The two ordered pairs that are solutions for the equation \( y = 4x - 2 \) are \( (2, 6) \) and \( (-1, -6) \).
1. For \( (-2, 0) \):
\[
y = 4(-2) - 2 = -8 - 2 = -10 \quad (\text{not } 0)
\]
2. For \( (2, 6) \):
\[
y = 4(2) - 2 = 8 - 2 = 6 \quad (\text{yes, this is a solution})
\]
3. For \( (-1, -6) \):
\[
y = 4(-1) - 2 = -4 - 2 = -6 \quad (\text{yes, this is a solution})
\]
4. For \( (6, 2) \):
\[
y = 4(6) - 2 = 24 - 2 = 22 \quad (\text{not } 2)
\]
The two ordered pairs that are solutions for the equation \( y = 4x - 2 \) are \( (2, 6) \) and \( (-1, -6) \).