Systems of linear equations and inequalities

9000026009

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?
\(\begin{aligned}2y -\phantom{ 2}x& < 4& \\x - 2y & < 2 \\ \end{aligned}\)
\(\begin{aligned}2y -\phantom{ 2}x& < 4& \\x - 2y & > 2 \\ \end{aligned}\)
\(\begin{aligned}2y - x& > 4 & \\2y - x& < -2 \\ \end{aligned}\)
\(\begin{aligned}2y - x& > 4 & \\2y - x& > -2 \\ \end{aligned}\)

9000026010

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?
\(\begin{aligned}x &\leq 3 & \\5x& < 9 - 3y \\ \end{aligned}\)
\(\begin{aligned}x & < 3 & \\5x& < 9 - 3y \\ \end{aligned}\)
\(\begin{aligned}x & > 3 & \\5x& < 9 - 3y \\ \end{aligned}\)
\(\begin{aligned}x &\leq 3 & \\5x& > 9 - 3y \\ \end{aligned}\)

9000023908

Level: 
A
Let \([x;y]\) be the solution of the system \[\begin{aligned} 2x - y & = -1, & & \\4x - y & = 1. & & \end{aligned}\] In the following list identify a true statement.
\(y\) is a prime number.
\(x\) is a prime number.
\(x + y\) is a prime number.
\(x - y\) is a prime number.