Which ordered pairs are solutions to the equation?
y = 3x – 4
A.
(11, 5) and (2, 2)
B.
(5, 11) and (3, 2)
C.
(5, 11) and (2, 3)
D.
(5, 11) and (2, 2)
To determine which ordered pairs are solutions to the equation y = 3x - 4, we need to substitute the values of x and y into the equation and check if the equation holds true.
Let's go through each option and substitute the x and y values:
A. (11, 5) and (2, 2)
For the pair (11, 5):
Substituting x = 11 and y = 5 into the equation y = 3x - 4:
5 = 3(11) - 4
5 = 33 - 4
5 = 29
The equation is NOT true, so (11, 5) is NOT a solution.
For the pair (2, 2):
Substituting x = 2 and y = 2 into the equation y = 3x - 4:
2 = 3(2) - 4
2 = 6 - 4
2 = 2
The equation is true, so (2, 2) is a solution.
Option A has only one solution, so it is NOT the correct answer.
B. (5, 11) and (3, 2)
For the pair (5, 11):
Substituting x = 5 and y = 11 into the equation y = 3x - 4:
11 = 3(5) - 4
11 = 15 - 4
11 = 11
The equation is true, so (5, 11) is a solution.
For the pair (3, 2):
Substituting x = 3 and y = 2 into the equation y = 3x - 4:
2 = 3(3) - 4
2 = 9 - 4
2 = 5
The equation is NOT true, so (3, 2) is NOT a solution.
Option B has only one solution, so it is NOT the correct answer.
C. (5, 11) and (2, 3)
For the pair (5, 11):
Substituting x = 5 and y = 11 into the equation y = 3x - 4:
11 = 3(5) - 4
11 = 15 - 4
11 = 11
The equation is true, so (5, 11) is a solution.
For the pair (2, 3):
Substituting x = 2 and y = 3 into the equation y = 3x - 4:
3 = 3(2) - 4
3 = 6 - 4
3 = 2
The equation is NOT true, so (2, 3) is NOT a solution.
Option C has only one solution, so it is NOT the correct answer.
D. (5, 11) and (2, 2)
For the pair (5, 11):
Substituting x = 5 and y = 11 into the equation y = 3x - 4:
11 = 3(5) - 4
11 = 15 - 4
11 = 11
The equation is true, so (5, 11) is a solution.
For the pair (2, 2):
Substituting x = 2 and y = 2 into the equation y = 3x - 4:
2 = 3(2) - 4
2 = 6 - 4
2 = 2
The equation is true, so (2, 2) is a solution.
Option D has two solutions, (5, 11) and (2, 2), which both satisfy the equation y = 3x - 4. Therefore, the correct answer is option D.
Basically, you are switching the 'x's and the 'y's, and then isolating to solve for x:
x= 3y-4
3y= x+4
y= (x+4)/3
Therefore y^-1 (that's how you write inverse) =(x+4)/3