A first number plus twice a second number is 1. Twice the first number plus the second totals 29. Find the numbers.

Question

Math 100 question. Part of homework assignment but could not figure it out. Thanks for helping. 

Answer 1

Hi Mason, let x represent the first number. Let y represent the second number.

 

Equation 1:

 

x + 2y = 1

 

Equation 2:

 

2x + y = 29

 

Solve by substitution for x:

 

x = -2y + 1

 

2 * (-2y + 1) + y = 29

 

-4y + 2 + y = 29

 

Combine terms:

 

-3y = 27

 

y = -9

 

Substitute for y in first equation:

 

x + 2 * -9 = 1

 

x - 18 = 1

 

x = 19

 

Solution:

 

x = 19

 

y = -9

 

Questions?