The lengths in inches (x and y) of two fish are related by the equation 5x – 4y = 24. The two ordered pairs that follow are solutions to the equation:
(4, -1) (12,9)
Which statement best evaluates whether these two solutions make sense in this situation?
A.
The solution (4, -1) makes sense in this situation, but (12,9) does not.
B.
Neither solution makes sense in this situation.
C.
Both solutions make sense in this situation.
D.
The solution (12,9) makes sense in this situation, but (4, -1) does not.
this is a really long one, and im having some trouble with it.
5x – 4y = 24.
5(4)-4(-1) = 24
20 + 4 = 24
24 = 24 true
5x – 4y = 24.
5(12) -4(9) = 24
60 -36 = 24
24 = 24
Answer C
Substitute the two number sets.
(5 * 4) - (4 * -1) = 24
20 + 4 = 24
That one makes sense.
What about 12 and 9?
To evaluate whether the given solutions make sense in this situation, we can substitute the ordered pairs into the equation and see if it holds true.
For the first solution (4, -1):
Substituting x = 4 and y = -1 into the equation 5x - 4y = 24:
5(4) - 4(-1) = 20 + 4 = 24
So, the equation holds true for the first solution.
For the second solution (12, 9):
Substituting x = 12 and y = 9 into the equation 5x - 4y = 24:
5(12) - 4(9) = 60 - 36 = 24
Again, the equation holds true for the second solution.
Therefore, both solutions (4, -1) and (12, 9) make sense in this situation.
So, the correct answer is C. Both solutions make sense in this situation.
To determine whether the given ordered pairs (4, -1) and (12, 9) make sense in the given situation, we need to consider the equation 5x - 4y = 24.
To check if a solution makes sense in this situation, we substitute the values of x and y from each ordered pair into the equation and see if the equation holds true.
For the ordered pair (4, -1):
Substituting x = 4 and y = -1 into the equation 5x - 4y = 24, we get:
5(4) - 4(-1) = 20 + 4 = 24.
Since the equation holds true for the pair (4, -1), this solution makes sense in the situation.
For the ordered pair (12, 9):
Substituting x = 12 and y = 9 into the equation 5x - 4y = 24, we get:
5(12) - 4(9) = 60 - 36 = 24.
Again, the equation holds true for the pair (12, 9), indicating that this solution also makes sense in the situation.
Both ordered pairs satisfy the equation, so the answer is:
C. Both solutions make sense in this situation.