Question 287278
Set-Up:
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Equation 1: {{{A + B = 11}}}
Equation 2: {{{10B + A + 45 = 10A + B}}}

Solution:
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Solve equation 1 for 1 of the variables
Equation 1: {{{A + B = 11}}}
{{{B = 11 - A}}}

Now Plug (11 - A) into equation 2 for B
Equation 2: {{{10B + A + 45 = 10A + B}}}
{{{10*(11 - A) + A + 45 = 10A + (11 - A)}}} Simplify
{{{110 - 10A + A + 45 = 10A + 11 - A}}} Combine like terms
{{{155 - 9A = 9A + 11}}} Subtract 11 from both sides
{{{144 - 9A = 9A}}} Add 9A to both sides
{{{144 = 18A}}} Divide both sides by 18
{{{highlight(8 = A)}}}

Now plug 8 into equation 1 for A
Equation 1: {{{A + B = 11}}}
{{{8 + B = 11}}}
{{{highlight(B = 3)}}}

So the origional number was {{{10A + B}}}
{{{10*8 + 3}}}
{{{highlight(83)}}}