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Part 1
A first number plus twice a second number is 12. Twice the first number plus the second totals 30. Find the numbers.

Answer 1

1st number = 12

2nd number = -6

We can solve this system of equations by isolating our variables and using substitution. We will let A be the first number and B be the second number, and we are going to isolate A in the first equation:

`A+B=12\\A=12-B`

Now we will plug this into our second equation:

`2A+B=30\\2(12-B)+B=30\\24-2B+B=30\\-B=6\\B=-6`

Next, we will plug B into our first equation where we isolated A:

`A=12-B\\A=12-(-6)\\A=18`

Now we have our values, A=18 and B=-6