SOLUTION: The sum of two numbers is 74. The second is 2 more than 3 times the first. What are the two numbers?

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Question 115334: The sum of two numbers is 74. The second is 2 more than 3 times the first. What are the two numbers?
Answer by aka042(26) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call our two numbers x and y.
We know that the sum of two numbers is 74, that is, x+%2B+y+=+74. We also know that the second number, y, is two more than 3 times the first number, x. That is to say y-2+=+3%2Ax, or y+-+3%2Ax+=+2.
Now we need to solve the system linearly:
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+74%2C%0D%0A++++-3%5Cx+%2B+1%5Cy+=+2+%29%0D%0A++

Any system of equations:


has solution

or



(x=18, y=56}



We conclude that your two numbers are 18 and 56. Let's just check to make sure. Is the sum of 55 and 19 74? Well, 55 + 19 = 74, so that agrees with the first part of the problem. Now, is 56 2 more than 3 * 18? Well, 3 * 18 = 54, and 54 + 2 = 56, therefore everything works out! Our two numbers are 18 and 56.