Strategy. Solve for one of the equations in terms of #x#, which will give an equation with only #y# on one side. Then, using the new "nickname" for #x#, plug the #y# expression into the other equation. Then solve for #y#. Then go back to the first equation and solve for #x#.
Step 1. Solve for one of the equations, getting #x=# an expression with #y#
#-7x-6y=-10#
Add #6y# to both sides.
#-7x=6y-10#
Divide both sides by #-7#. This is the "nickname" for #x#.
#x=-(6)/(7)y+10/7#
Step 2. Plug this "nickname" for #x# into the other equation.
#3color(red)(x)+4y=10#
Replace #x# with it's "nickname".
#3(color(red)(-(6)/(7)y+10/7))+4y=10#
Multiply #3# through.
#-18/7 y+30/7+4y=10#
Multiply everything by #7#.
#-18y+30+28y=70#
Combine like terms and solve for #y#.
#10y=40#
#y=4#
Step 3. Plug #y=4# back into the "nickname" for #x#.
#x=-(6)/(7)color(red)(y)+10/7#
#x=-(6)/(7)xxcolor(red)(4)+10/7#
#x=-(24)/(7)+10/7=-(14)/7=-2#
ANSWER: #x=-2# and #y=4#
