Question

which of these ordered pairs is a solution to this equation? y = 3x − 1 (4, 11) (2, 7)

Explanation:

Step1: Check (4, 11)

Substitute \( x = 4 \) into \( y = 3x - 1 \). Then \( y = 3\times4 - 1 = 12 - 1 = 11 \), which matches the \( y \)-value of the ordered pair (4, 11).

Step2: Check (2, 7)

Substitute \( x = 2 \) into \( y = 3x - 1 \). Then \( y = 3\times2 - 1 = 6 - 1 = 5 \), which does not match the \( y \)-value of 7 in the ordered pair (2, 7). Wait, there was a miscalculation above. Let's recalculate for (2,7):

Step1 (revised for (2,7)): Check (2, 7)

Substitute \( x = 2 \) into \( y = 3x - 1 \). So \( y = 3(2)-1 = 6 - 1 = 5
eq 7 \). So (2,7) is not a solution.

Step1 (correct for (4,11)): Check (4, 11)

Substitute \( x = 4 \) into \( y = 3x - 1 \). \( y = 3(4)-1 = 12 - 1 = 11 \), which matches the \( y \)-coordinate of (4,11). So (4,11) is a solution.

Wait, the initial check for (2,7) had an error. Let's present the correct steps:

Step1: Check (4, 11)

For the equation \( y = 3x - 1 \), when \( x = 4 \), calculate \( y \):
\( y = 3(4) - 1 = 12 - 1 = 11 \).
Since the calculated \( y \) (11) matches the \( y \)-value of the ordered pair (4, 11), (4, 11) is a solution.

Step2: Check (2, 7)

For the equation \( y = 3x - 1 \), when \( x = 2 \), calculate \( y \):
\( y = 3(2) - 1 = 6 - 1 = 5 \).
Since the calculated \( y \) (5) does not match the \( y \)-value of the ordered pair (2, 7) (which is 7), (2, 7) is not a solution.

So the correct answer is (4, 11) as the solution to \( y = 3x - 1 \).

Answer:

(4, 11) and (2, 7) (We will check each ordered pair below)