Question

The sum of two numbers is 12 and their difference is 4.

Type your answer using only numerals (i.e., 1, 2, 4.5) and, if needed, a negative sign (i.e., -3, -0.4, -105).

The largest value of the two numbers is

Answer 1

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.