Plug the values (x,y)=(2,2) into the equations and check if they satsify them.
a.
[tex]-3x+3y=0 \\
x+6y=10 \\ \\
\hbox{the first equation:} \\
-3 \times 2+3 \times 2=0 \\
-6+6=0 \\
0=0 \\
true \\ \\
\hbox{the second equation:} \\
2+6 \times 2=10 \\
2+12=10 \\
14=10 \\
false \\ \\
\hbox{(2,2) satisfies only one of the equations} \\
\hbox{so it's not a solution to the system of equations}[/tex]
b.
[tex]-2x+5y=-6 \\
4x-2y=4 \\ \\
\hbox{the first equation:} \\
-2 \times 2 + 5 \times 2=-6 \\
-4+10=-6 \\
6=-6 \\
false \\ \\
\hbox{the second equation:} \\
4 \times 2-2 \times 2=4 \\
8-4=4 \\
4=4 \\ true \\ \\
\hbox{(2,2) satisfies only one of the equations} \\
\hbox{so it's not a solution to the system of equations}[/tex]
c.
[tex]5x-2y=-6 \\
3x-4y=2 \\ \\
\hbox{the first equation:} \\
5 \times 2 - 2 \times 2=-6 \\
10-4=-6 \\
6=-6 \\
false \\ \\
\hbox{the second equation:} \\
3 \times 2 - 4 \times 2=2 \\
6-8=2 \\
-2=2 \\
false \\ \\
\hbox{(2,2) satisfies none of the equations} \\
\hbox{so it's not a solution to the system of equations}[/tex]
d.
[tex]2x+3y=10 \\
4x+5y=18 \\ \\
\hbox{the first equation:} \\
2 \times 2 + 3 \times 2=10 \\
4+6=10 \\
10=10 \\
true \\ \\
\hbox{the second equation:} \\
4 \times 2 + 5 \times 2 =18 \\
8+10=18 \\
18=18 \\ \\
\hbox{(2,2) satisfies both of the equations} \\
\hbox{so it is a solution to the system of equations}[/tex]
The answer is D.
