Answer:(3,4)Step-by-step explanation:The system of equations is:x+6y=277x-3y=9.I looked up "metodo de igualacion". It is basically American for doing substitution. However, the only difference is you are asked to solve both equations for a variable. The first equation looks easy to solve for x. So I'm going to solve both equations for x.x+6y=27Subtract 6y on both sides:x =-6y+277x-3y=9 Add 3y on both sides:7x =3y+9 Divide both sides by 7: x =3/7 y +9/7So both equations are solved for x. You want to find when the x's are the same because you are looking for a common amongst the lines given.So we have-6y+27=3/7 y +9/7I hate the fractions honestly so I'm going to multiply both sides by 7 so they will no longer be for now:-42y+189=3y + 9Now add 42y on both sides: 189=45y+9Subtract 9 on both sides: 180=45yDivide both sides by 45: 4=yIf 4=y, then y=4.So now once we have obtain 4 for y, we will use one of the equations given along with it to find x. Just choose one. Choose the easier looking one to you.I like the x=-6y+27 with y=4.So replace y with giving you:x=-6(4)+27x=-24+27x=3So the solution is (x,y)=(3,4).x=3 and y=4.