Question

The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number, what are the two numbers?
a: x=-5, y=-8
b: x=-8, y=-5
c: x=8, y=5
d: x=5, y=8

Answer 1

Solving this problem will require a system of equations. Since it's already assigned variables, we can make the equations. They are as follows.

x + y = 13    (The sum of the two numbers, x and y, is 13.)
2x - 3y = 1    (Two times the first number minus three times the second number is 1.)

To solve this system using the substitution method, isolate either x or y in the first equation. I'll isolate y.

    x + y = 13
          y = 13 - x

Substitute 13 - x for y into the second equation and solve algebraically for x.

    2x - 3y = 1
    2x - 3(13 - x) = 1
    2x - 39 + 3x = 1
    5x - 39 = 1
    5x = 40
    x = 8

Substitute 8 for x into either of the original equations and solve algebraically for y.

    x + y = 13
    8 + y = 13
    y = 5

Check all work by plugging the x- and y-values accordingly into each equation.

    x + y = 13  =>  8 + 5 = 13
    2x - 3y = 1  =>  2(8) - 3(5) = 1  =>  16 - 15 = 1

Answer:
c: x = 8, y = 5

(8, 5)