x - the number of the questions worth 2 points
y - the number of the questions worth 4 points
[tex]x+y=50 \\
2x+4y=110 \\ \\
\hbox{from the 1st equation:} \\
y=50-x \\ \\
\hbox{substitute 50-x for y in the 2nd equation:} \\
2x+4(50-x)=110 \\
2x+200-4x=110 \\
-2x=-90 \\
x=45 \\ \\
y=50-45=5[/tex]
The answer:
There are 45 questions worth 2 points and 5 questions worth 4 points.