Question 309420
Set-Up:
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Equation 1: {{{A + B = 7}}}
Equation 2: {{{10A + B + 9 = A + 10B}}}
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Solution:
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Solve equation 1 for one of the variables
I solved for B
Equation 1: {{{A + B = 7}}}
{{{B = 7 - A}}}
Now plug (7 - A) into equation 2 for B
Equation 2: {{{10A + B + 9 = A + 10B}}}
{{{10A + (7 - A) + 9 = A + 10*(7 - A)}}} Simplify
{{{10A + 7 - A + 9 = A + 70 - 10A}}} Simplify
{{{9A + 16 = 70 - 9A}}} Add 9A to both sides
{{{18A + 16 = 70}}} Subtract 16 from both sides
{{{18A = 54}}} Divide both sides by 18
{{{highlight(A = 3)}}}
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Now plug 3 into equation 1 for A
{{{B = 7 - A}}}
{{{B = 7 - 3}}}
{{{highlight_green(B = 4)}}}