Question

Write and solve a system of equations. Be sure to label the variables. The sum of two numbers is fourteen. Two times the first number plus three times the second number is nine. What are the two numbers? Show and Explain all work.

Answer 1

First number = 33, Second number = -19

Explanation:

We can use F to represent the first number and S to represent the second number.

Our two equations then are F + S = 14 and 2F + 3S = 9

We can use substitution:

`F+S = 14\\2F+3S=9\\F=14-S\\2(14-S)+3S=9\\28-2S+3S=9\\28+S=9\\S=-19\\\\F-19=14\\F=33`