Question 689964
Given:{{{4X +3Y = -4}}} & {{{3X - 7Y = 34}}}
Set both equations equal to zero
{{{4X + 3Y + 4 =0}}} & {{{3X - 7Y - 34 = 0}}}
Multiply the first equation by 3
{{{12X + 9Y + 12 = 0}}}
Multiply the second equation by 4
{{{12X - 28Y - 136 = 0}}}
We did that multiplication to get the X variables to a common number (12)
Since both equations equal zero, we can set them equal to each other
{{{12X + 9Y + 12 = 12X  - 28Y - 136}}}
Subtract 12X from both sides
{{{9Y + 12 = -28Y - 136}}}
Add 28Y to both sides
{{{37Y + 12 = -136}}}
Subtract 12 from both sides
{{{37Y = -148}}}
Divide both sides by 37
{{{highlight(Y = -4)}}}
-----------------------
Now plug -4 into one of the given equations for Y
{{{4X +3Y =-4}}}
{{{4X + 3*(-4) = -4}}}
{{{4X - 12 = -4}}}
Add 12 to both sides
{{{4X = 8}}}
Divide both sides by 4
{{{highlight_green(X = 2)}}}