Substitution/Elimination Word Problems

Question

Your friend is trying to see if you can guess the two numbers she secretly has written on her paper. Your friend tells you that 2 times the first number is 13 more than the second number. She also tells you that the sum of the two numbers is 62. Can you guess your friends numbers?

Answer 1

First number is x

second number is y

2x = 13 + y 

2x - y = 13   (rearranging)

x + y = 62

 

Add both equatuons together cuz y has the same coefficient and opposite signs 

 

3x + 0 = 75

x = 75/3

x = 25

 

from the second equation: y = 62 - x

y = 62 - 25

y = 37