Question

Solve the problems using systems of equations.

The sum of two numbers is 5. The difference of the numbers is -3. Find the two numbers.

Answer 1

Explanation:

Let the two numbers be x and y

x+y =5 ---1

x-y =-3 ---2

Rearrange equation 1

x =5-y

Substitute x in the second equation

(5-y)-y =-3

5-y-y =-3

5-2y =-3

Collect like terms

5+3 = 2y

8 = 2y

Divide both sides by the coefficient of y (2)

8/2 = 2y/2

4 = y

y= 4

Substitute y in equation 1

x+4 =5

Subtract 4 from both sides

x+4-4 = 5-4

x+0 = 1

x= 1

The two numbers are 1 and 4