Question

Write a system of equations and solve using elimination The sum of two numbers is 18. The difference between the two numbers is 2. What are the two numbers?

Answer 1

Assume that the 2 numbers are x and y, then

Since their sum is 18

That means add x and y, equate the sum by 18

$x+y=18(1)$

Since their difference is 2

That means subtract x and y, equate the difference by 2

$x-y=2(2)$

Add (1) and (2) to eliminate y

$\begin{gathered} (x+x)+(y-y)=(18+2) \\ 2x+0=20 \\ 2x=20 \end{gathered}$

Divide both sides by 2 to find x

$\begin{gathered} \frac{2x}{2}=\frac{20}{2} \\ x=10 \end{gathered}$

Substitute the value of x in (1) to find y

$10+y=18$

Subtract 10 from both sides

$\begin{gathered} 10-10+y=18-10 \\ y=8 \end{gathered}$

The 2 numbers are 10 and 8