Question 695908
Given: {{{2X + 5Y = 12}}} and {{{-4X + 4Y = 18}}}
Start by setting the equations equal to zero.
{{{2X + 5Y - 12 = 0}}} and {{{-4X + 4Y - 18 = 0}}}
Multiply the first equation by -2
{{{-4X - 10Y + 24 = 0}}}
Since both eqautions are equal to zero, you can set them equal to each other.
{{{-4X - 10Y + 24 = -4X + 4Y - 18}}}
Add 4X to both sides
{{{-10Y + 24 = 4Y - 18}}}
Add 10Y to both sides
{{{24 = 14Y - 18}}}
Add 18 to both sides
{{{42 = 14Y}}}
Divide both sides by 14
{{{highlight(3 = Y)}}}
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Now plug 3 into one of the given equations for Y
{{{2X + 5Y = 12}}} 
{{{2X + 5*(3) = 12}}}
{{{2X + 15 = 12}}}
Subtract 15 from both sides
{{{2X = -3}}}
Divide both sides by 2
{{{highlight_green(-1.5 = X)}}}