Let's look at the first equation:
[tex]3y=x+y+9[/tex]
We'll write the variable y in terms of x and then the variable x in terms of y. First:
[tex]3y-y=x+9[/tex][tex]2y=x+9[/tex]
From here:
[tex]y=\frac{x+9}{2}[/tex]
and
[tex]x=2y-9[/tex]
Doing a similar procedure with the other two equations we'll get:
From
[tex]3y+x=y+6[/tex][tex]y=3-\frac{x}{2}[/tex]
and
[tex]x=6-2y[/tex]
From
[tex]x+y+4x=16+2x[/tex][tex]y=16-3x[/tex]
and
[tex]x=\frac{16-y}{3}[/tex]
In sumary, let's go over each of the equations and check that the values we got are correct.
From the equation
[tex]3y=x+y+9[/tex]
The answers we got are:
[tex]y=\frac{x+9}{2}[/tex][tex]x=2y-9[/tex]
Let's plug these values in the equation to verify our result
[tex]3(\frac{x+9}{2})=2y-9+\frac{x+9}{2}+9[/tex]
Doing all the operations we'll get:
[tex]y=\frac{x+9}{2}[/tex]
Which is what we started with, so the solutions are correct.
Similarly, for the equation
