Question

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.

According to the problem, the sum of the two numbers is 10, so we can write the equation:

x + y = 10 ----(1)

The problem also states that the difference between the two numbers is 6, so we can write the equation:

x - y = 6 ----(2)

Now we have a system of two equations:

x + y = 10 ----(1)
x - y = 6 ----(2)

To determine the solution without graphing, we can use the method of substitution. From equation (2), we can solve for x in terms of y:

x = y + 6

Now we substitute this expression for x into equation (1):

(y + 6) + y = 10

Combine like terms:

2y + 6 = 10

Subtract 6 from both sides:

2y = 4

Divide both sides by 2:

y = 2

Now that we know y = 2, we can substitute this value back into equation (2) to solve for x:

x - 2 = 6

Add 2 to both sides:

x = 8

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