Solve the problem using the elimination method.
-The sum of two numbers is 8. Four times the larger number plus two times the smaller number is 66. Find the numbers.
A)17 and -9
B)17 and -25
C)25 and -17
D)33 and -25

Question

Quizplus · Accepted Answer

Let's call the larger number x and the smaller number y. 
From the first sentence, we know that: 
x + y = 8 
From the second sentence, we know that: 
4x + 2y = 66 
Now, we can use the elimination method by multiplying the first equation by 2 and subtracting it from the second equation:

(4x + 2y = 66) - 2(x + y = 8) 
Simplifying: 
4x + 2y = 66 - 2x - 2y = 62 
Combining like terms: 
2x = 4 
x = 2

Now, we can substitute x=2 into either of the two original equations to solve for y:

2 + y = 8 
y = 6

So the two numbers are x=2 and y=6. However, this is not one of the answer choices. We need to check if one of the answer choices can be obtained by switching the values of x and y (since the problem did not specify which number is larger).

If we switch x and y, we get: 
x + y = 8 
2x + 4y = 66

Multiplying the first equation by 2 gives: 
2x + 2y = 16

Subtracting this from the second equation gives: 
2y = 50 
y = 25

Now, we can substitute y=25 into either of the two original equations to solve for x:

x + 25 = 8 
x = -17

So the two numbers are x=-17 and y=25, which matches answer choice C. Let x be the larger number and y be the smaller number. From the first equation, we have:
x + y = 8
From the second equation, we have:
4x + 2y = 66
We can eliminate y by multiplying the first equation by -2 and adding it to the second equation:
-2(x + y) + 4x + 2y = -16 + 66
2x = 50
x = 25
Substituting x = 25 into the first equation, we have:
25 + y = 8
y = -17
Therefore, the numbers are 25 and -17, which corresponds to choice C.

Solve the Problem Using the Elimination Method