5. Write a system of equations where the sum of two numbers is 10 and the difference is 6. Can you determine the solution without graphing? Guess and check.

Answer 1

Let's call the two numbers x and y.

The first equation states that the sum of the two numbers is 10:

x + y = 10

The second equation states that the difference between the two numbers is 6:

x - y = 6

To solve this system of equations without graphing, we can use the method of substitution or elimination.

Using the substitution method, we can solve the second equation for x:

x = y + 6

Now we can substitute this expression for x in the first equation:

(y + 6) + y = 10

Simplifying:

2y + 6 = 10

Subtracting 6 from both sides:

2y = 4

Dividing both sides by 2:

y = 2

Now we can substitute this value for y back into the second equation to find x:

x - 2 = 6

Adding 2 to both sides:

x = 8

Therefore, the solution to the system of equations is x = 8 and y = 2.