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

Answer 1

Steps:

So for this, we will be setting up a system of equations with the information we have:

$x+y=13\ \textsf{"The sum of two numbers is 13."}\\2x-3y=1\ \textsf{"Two times the first number minus three times the second number is 1."}$

Now we have our system of equations set up. Next, I will be using the substitution method to solve this system. So firstly, subtract y on both sides of the first equation:

$x=13-y\\2x-3y=1$

Now, substitute x for (13 - y) in the second equation and solve for y as such:

$2(13-y)-3y=1\\26-2y-3y=1\\26-5y=1\\-5y=-25\\y=5$

Now that we have the value of y, substitute it into either equation to solve for x:

$x+5=13\\x=8\\\\2x-3(5)=1\\2x-15=1\\2x=16\\x=8$

Answer:

In short, the first number (x) is 8 and the second number (y) is 5.