Question 291126
"the sum of two numbers is 23" means that {{{x+y=23}}} and "twice the greater number added to three times the smaller number is 57" tells us that {{{2x+3y=57}}}. Here we're assuming that 'x' is the greater number.



{{{x+y=23}}} Start with the first equation.



{{{y=-x+23}}} Solve for 'y' by subtracting 'x' from both sides.



{{{2x+3y=57}}} Move onto the second equation.



{{{2x+3(-x+23)=57}}} Plug in {{{y=-x+23}}}



{{{2x-3x+69=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+23}}} Go back to the equation previously solved for 'y'.



{{{y=-12+23}}} 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.