SOLUTION: the question is ... the sum of two numbers is 23. twice the greater number added to three times the smaller number is 57. find the numbers

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Question 291126: the question is ... the sum of two numbers is 23. twice the greater number added to three times the smaller number is 57. find the numbers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"the sum of two numbers is 23" means that x%2By=23 and "twice the greater number added to three times the smaller number is 57" tells us that 2x%2B3y=57. Here we're assuming that 'x' is the greater number.


x%2By=23 Start with the first equation.


y=-x%2B23 Solve for 'y' by subtracting 'x' from both sides.


2x%2B3y=57 Move onto the second equation.


2x%2B3%28-x%2B23%29=57 Plug in y=-x%2B23


2x-3x%2B69=57 Distribute


2x-3x=57-69 Subtract 69 from both sides.


-x=-12 Combine like terms.


x=12 Divide both sides by -1 to isolate 'x'


y=-x%2B23 Go back to the equation previously solved for 'y'.


y=-12%2B23 Plug in x=12


y=11 Add


So the solutions are x=12 and y=11 which means that the two numbers are 12 and 11.