One number is 2 more than 3 times another. Their product is 5 more than 2 times their sum. Find the numbers.

Question

solving equations

 

Answer 1

Jennifer,

 

1st number is x

2nd number is y

 

x = 3y + 2 (one number is 2 more than 3 times another)

xy = 2(x + y) + 5 (product is 5 more than 2 times their sum)

 

Solve these equations by substitution of x in the second equation:

(3y + 2)y = 2(3y + 2 + y) + 5

 

3y² + 2y = 6y + 4 + 2y + 5

 

3y² + 2y = 8y + 9

 

3y² + 2y - 8y - 9 = 0

 

3y² - 6y - 9 = 0

 

You need to factor this quadratic equation: 

3(y² - 2y - 3) = 0

 

(y -3) (y + 1) = 0

 

y = 3 or -1

 

If y = 3, x =3(3) + 2 = 11

If y = -1, x = 3(-1) + 2 = -1

 

Therefore the solution is x = 11, y = 3  and x = -1, y = -1

 

Hope it helps