Answer:
The largest value of the two numbers is 8.
Explanation:
We can find the largest value of the two numbers using a system of equations where:
- x represents one number,
- and y represents the other number.
We'll first need to determine the two numbers and then we can compare them.
First equation:
Since the sum of the two numbers is 12, our first equation is given by:
x + y = 12
Second equation:
Since the difference of the two numbers is 4, our second equation is given by:
x - y = 4
Method to solve: Elimination:
Solving for x:
Adding the two equations will allow us to solve for x and eliminate y since y - y = 0:
x + y = 12
+
x - y = 4
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(x + x) + (y - y) = (12 + 4)
(2x = 16) / 2
x = 8
Thus, one of the numbers is 8.
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- We technically don't have to find the other number since only 8 + 4 = 12, meaning the other number is 4 and 8 is the larger of the two values.
- However, I'll find it still to check that the answer is correct.
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Solving for y:
Now, we can solve for y by plugging in 8 for x in x + y = 12:
(8 + y = 12) - 8
y = 4
Thus, the other number is 4.
Therefore, 8 is the largest value of the two numbers.