The larger of two numbers is two more than three times the smaller.And when the larger number is subtracted from the smaller, the result is -16. What are the two numbers.
x = larger number
y = smaller number
The larger number of two numbers (x) is (=) two more (2 +) than three time (3X) the smaller (y).
x = 2 + 3y
When the larger number (x) is subtracted (- before the x) from the smaller (y), the result is (=) -16.
y - x = -16
Now that we have created two equations in two variables, we can solve the equations for the answer. I will used substitution.
y - x = -16 Equation 2
y - (2 + 3y) = -16 Substitute the value of x in equation 1 for x in equation 2
y - 2 - 3y = -16 Distributive property
-2y - 2 = -16 Simplify
-2y - 2 + 2 = -16 + 2 Add 2 to each side
- 2y = -14 Simplify
-2y/(-2) = -14/(-2) Divide each side by -2
y = 7 Simplify
x = 2 + 3y Equation 1
x = 2 + 3(7) Substitution
x = 2 + 21 Simplify
x = 23
The larger number is 23 and the smaller number is 7.