#5x+7y=6# and #2x-3y=11#
Let's make an equation for #x# out of the second equation. We will do this by isolating the #x#:
#2x=3y+11#
#\color(maroon)(x=3/2y+11/2)#
Let's plug this into the first equation, #5\color(maroon)(x)+7y=6#.
#5(\color(maroon)(3/2y+11/2))+7y=6#
#5(3/2y)+5(11/2)+7y=6# Applying Distributive Property
#15/2y+55/2+7y=6# Simplifying.
#15/2y+55/2+14/2y=12/2# Make everything have equivalent denominators
#\color(seagreen)(15/2y+14/2y)=\color(slateblue)(-55/2+12/2)# Identify like terms; make sure you place the variable terms alone on one side
#\color(seagreen)(29/2y)=\color(slateblue)(-43/2)# Simplifying.
Since both sides have denominator 2, just remove it from the equation. Now we have #29y=-43#, which you can just divide to get y.
#y=-43/29\approx-1.483#
Now we take that y-value and plug it back into the equation we found for #x#:
#x=3/2(\color(fuchsia)(-1.483))+11/2#
#x\approx3.276#
