Question 699550
Given: {{{5A - B = 12}}} and {{{7A - 3B = 20}}}
Set both equations equal to zero
{{{5A - B - 12 = 0}}}
{{{7A - 3B - 20 = 0}}}
Notice that you can make both equations contain -3B if you multiply the first equation by 3.
{{{3*(5A - B - 12) = 3*0}}}
Simplify
{{{15A - 3B - 36 = 0}}}
Now both equations have a -3B in them.
Since both equations are equal to zero, you can set them equal to each other.
{{{15A - 3B - 36 = 7A - 3B - 20}}}
Add 3B to both sides
{{{15A - 36 = 7A - 20}}}
Subtract 7A from both sides
{{{8A - 36 = -20}}}
Add 36 to both sides
{{{8A = 16}}}
Divide both sides by 8
{{{highlight(A = 2)}}}
Now plug 2 into on of the given equations for A. Then solve for B
{{{5A - B = 12}}}
{{{5*(2) - B = 12}}}
{{{10 - B = 12}}}
Subtract 10 from btoh sides
{{{-B = 2}}}
Divide both sides by -1
{{{highlight_green(B = -2)}}}