Question

The sum of two numbers is 18. Their difference is -8. Find the two numbers.

Part A
Write a system of equations that represents the situation.
x + y =
x-y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.

Answer 1

When we write out the system of equations, we will get:

`x+y=18`

`x-y=-8`

We can then use elimination to get just one variable.

`x+y=18`

`x-y= -8`

Which gives us:
`2x=10`

We then divide by 2 and get:
`x=5`

We next plug that into one of the two equations and solve for the other variable:
`(5)+y=18`

We subtract 5 from both sides and get:
`y=13`

So the two numbers are 13 and 5.