Question 698139
Given: {{{X - 2Y = 12}}}
& {{{4X + 2Y = 8}}}
Set both equations equal to zero
{{{X - 2Y -12 = 0}}}
{{{4X + 2Y - 8 = 0}}}
Notice that both equations contain a 2Y.
You need to multiply on of the equations by -1 to make the signs of the 2Y match
I choose the first one.
{{{-X + 2Y + 12 = 0}}}
Since both equations equal zero, you can set the equations equal to each other.
{{{-X + 2Y + 12 = 4X + 2Y - 8}}}
Subtract 2Y from both sides
{{{-X + 12 = 4X - 8}}}
Add 8 to both sides
{{{-X + 20 = 4X}}}
Add X to both sides
{{{20 = 5X}}}
Divide both sides by 5
{{{highlight(4 = X)}}}
Now plug 4 into one of the equations for X and solve for Y
{{{X - 2Y = 12}}}
{{{4 - 2Y = 12}}}
Add 2Y to both sides
{{{4 = 12 + 2Y}}}
Subtract 12 from both sides
{{{-8 = 2Y}}}
Divide both sides by 2
{{{highlight_green(-4 = Y)}}}