Question

Find two rational numbers such that the sum of the first number and four times the second number is 3, and the sum of four times the second number and two times the first number is 5. What are these two rational numbers?

Answer 1

To solve for two rational numbers that fit the given conditions, we set up a system of linear equations and solved for x and y. The two rational numbers satisfying the conditions are x = 2 and y = 1/4.

Step-by-step explanation:

To find two rational numbers that satisfy the given conditions, we need to set up a system of equations based on the information provided. Let the first number be x and the second number be y. The first condition states that the sum of the first number and four times the second number is 3, which can be written as x + 4y = 3. The second condition states that the sum of four times the second number and two times the first number is 5, which can be written as 4y + 2x = 5. To solve this system, we can follow these steps:

1. Write the two equations:
   x + 4y = 3 (Equation 1)
   2x + 4y = 5 (Equation 2)
2. Subtract Equation 1 from Equation 2 to eliminate y:
   2x - x = 5 - 3
   x = 2
3. Substitute x = 2 into Equation 1 to find y:
   2 + 4y = 3
   4y = 1
   y = 1/4

Therefore, the two rational numbers are x = 2 and y = 1/4.