Associated Topics || Dr. Math Home || Search Dr. Math

```
Date: 04/08/97 at 18:40:09
From: Aaron Hubert
Subject: Solving a system of two equations

I have a word problem that I haven't even started because I don't
understand it.

"The sum of two numbers is 15 and their product is 54. Find the

Any help would be deeply appreciated.
```

```
Date: 04/13/97 at 12:20:51
From: Doctor Steven
Subject: Re: Solving a system of two equations

You have those two equations to solve for. Say the first number is x,
and the second number is y. Then:

x + y = 15
x * y = 54.

Using the first equation:

y = 15 - x.

Plug this into the second equation to get

x*(15 - x) = 54.

Simplify the equation:

15x - x^2 = 54.

Simplify more:

x^2 - 15x + 54 = 0.

Solve for x using the quadratic equation.  Then y = 15 - x.

Hope this helps.

-Doctor Steven,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Linear Equations
Middle School Algebra
Middle School Equations

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search