The difference between the squares of two numbers is 3 Three

The difference between the squares of two numbers is 3. Three times the square of the first number increased by the square of the second number is 13. Find the numbers. The numbers are (Type ordered pairs. Use a comma to separate answers.)

Solution

Let the two numbers be x and y

According to the question

x²-y²=3

2x²-y²=13

Subtracting both equations

x²=10

x=+-sqrt10

When x=+_sqrt10, y=+-sqrt7

Solution set (-sqrt10,-sqrt7),(-sqrt10,sqrt7),(sqrt10,-sqrt7),(sqrt10,sqrt7)