Which of the following is a solution to the equation y = 3x – 1?
(4, 1)
(2, 5)
(4, 3)
(0, –3)
To determine which of the given ordered pairs is a solution to the equation y = 3x - 1, we substitute the values of x and y into the equation.
For the first ordered pair (4, 1):
y = 3x - 1
1 = 3(4) - 1
1 = 12 - 1
1 = 11
This equation is not true, so (4, 1) is not a solution to the equation.
For the second ordered pair (2, 5):
y = 3x - 1
5 = 3(2) - 1
5 = 6 - 1
5 = 5
This equation is true, so (2, 5) is a solution to the equation.
For the third ordered pair (4, 3):
y = 3x - 1
3 = 3(4) - 1
3 = 12 - 1
3 = 11
This equation is not true, so (4, 3) is not a solution to the equation.
For the fourth ordered pair (0, -3):
y = 3x - 1
-3 = 3(0) - 1
-3 = 0 - 1
-3 = -1
This equation is not true, so (0, -3) is not a solution to the equation.
Therefore, the only solution to the equation y = 3x - 1 is (2, 5).
To find the solution to the equation y = 3x - 1, we need to substitute the given x-values into the equation and check if the resulting y-values match.
Let's check each option:
For the first option (4, 1):
y = 3x - 1
1 = 3(4) - 1
1 = 12 - 1
1 = 11
The resulting y-value does not match, so (4, 1) is not a solution to the equation.
For the second option (2, 5):
y = 3x - 1
5 = 3(2) - 1
5 = 6 - 1
5 = 5
The resulting y-value matches, so (2, 5) is a solution to the equation.
For the third option (4, 3):
y = 3x - 1
3 = 3(4) - 1
3 = 12 - 1
3 = 11
The resulting y-value does not match, so (4, 3) is not a solution to the equation.
For the fourth option (0, -3):
y = 3x - 1
-3 = 3(0) - 1
-3 = 0 - 1
-3 = -1
The resulting y-value does not match, so (0, -3) is not a solution to the equation.
Therefore, the only solution to the equation y = 3x - 1 is (2, 5).
To find the solutions to the equation y = 3x - 1, you need to substitute the values of x from each option and check if the equation holds true.
Let's go through each option:
(4, 1): Substitute x = 4 into the equation:
y = 3(4) - 1
y = 12 - 1
y = 11
Since the equation states y = 11, the point (4, 1) is not a solution to the equation y = 3x - 1.
(2, 5): Substitute x = 2 into the equation:
y = 3(2) - 1
y = 6 - 1
y = 5
Since the equation states y = 5, the point (2, 5) is a solution to the equation y = 3x - 1.
(4, 3): Substitute x = 4 into the equation:
y = 3(4) - 1
y = 12 - 1
y = 11
Since the equation states y = 3, the point (4, 3) is not a solution to the equation y = 3x - 1.
(0, -3): Substitute x = 0 into the equation:
y = 3(0) - 1
y = 0 - 1
y = -1
Since the equation states y = -1, the point (0, -3) is not a solution to the equation y = 3x - 1.
Therefore, the only solution to the equation y = 3x - 1 is the point (2, 5).