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)
