The sum of two numbers is 57.4. One number is six times the other. Find the numbers?

a + b = 57.4 "The sum of two numbers is 57.4"

b = 6a "One number is six times the other."

You have two lines. It looks like this: www.wolframalpha.com/input/?i=plot+a+%2B+b+%3D+57.4,+b+%3D+6a

Where they cross, the values of x and y satisfy both equations simultaneously, so it is called a simultaneous system. There are two ways to find that point. Substitution is when you solve one equation for one variable and substitute that into the other equation. Since we are given b=6a we will substitute that into the other equation.

a + 6a = 57.4

a = 57.4/7 = 8.2 Put this into either original equation to find a value for b.

b = 49.2

www.wolframalpha.com/input/?i=solve+a+%2B+b+%3D+57.4,+b+%3D+6a

Elimination is when you add the equations in a way to eliminate one variable. Otherwise the process is the same.