The difference of two numbers is -1. If twice the first number is added to three times the second number, the result is 13. What are the numbers?

Question

Algebra II

Answer 1

"The difference of two numbers is -1." is written as x -y = -1 . Our key words are difference, which means subtraction and is, which is equals.

"If twice the first number is added to three times the second number, the result is 13." is written as

2x + 3y = 13 . rewrite x - y = -1 as x = y-1 then substitute into the other equation.

2(y-1) + 3y = 13

2y -2 + 3y = 13

5y - 2 = 13

5y= 15

y = 3

then substitute y into the original equation to get x

x-y= -1

x - 3 = -1

x = 2

so your solution set for (x,y) is (2,3)