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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

User Tom Shaw
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1 Answer

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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)
User Maxim Lazarev
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