9000026003
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
2x - y\geq &2 & &
\\2x + y\geq & - 2 & &
\end{aligned}\]
yellow
red
green
blue
Systems of linear equations and inequalities
9000026004
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
2y - x\geq &4 & &
\\2y - x\geq & - 2 & &
\end{aligned}\]
blue
red
yellow
9000026005
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x\leq &3 & &
\\5x > &9 - 3y & &
\end{aligned}\]
yellow
red
green
blue
9000026006
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?
\(\begin{aligned}x +\phantom{ 2}y&\geq 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y& > 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y&\leq 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y& < 3 &
\\y - 2x& > -1
\\ \end{aligned}\)
9000026007
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?
\(\begin{aligned}y & < 2 &
\\y + 1&\geq x + 1
\\ \end{aligned}\)
\(\begin{aligned}y &\geq 2 &
\\y + 1& < x + 1
\\ \end{aligned}\)
\(\begin{aligned}y & > 2 &
\\y + 1&\leq x + 1
\\ \end{aligned}\)
\(\begin{aligned}y&\leq 2 &
\\y& > x
\\ \end{aligned}\)
9000026008
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?
\(\begin{aligned}2x - y&\leq 2 &
\\2x + y&\geq - 2
\\ \end{aligned}\)
\(\begin{aligned}2x - y&\geq 2 &
\\2x + y&\geq - 2
\\ \end{aligned}\)
\(\begin{aligned}2x - y&\leq 2 &
\\2x + y&\leq - 2
\\ \end{aligned}\)
\(\begin{aligned}2x - y&\geq 2 &
\\2x + y&\leq - 2
\\ \end{aligned}\)
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?
\(\begin{aligned}x &\leq 3 &
\\5x& < 9 - 3y
\\ \end{aligned}\)
\(\begin{aligned}x & < 3 &
\\5x& < 9 - 3y
\\ \end{aligned}\)
\(\begin{aligned}x & > 3 &
\\5x& < 9 - 3y
\\ \end{aligned}\)
\(\begin{aligned}x &\leq 3 &
\\5x& > 9 - 3y
\\ \end{aligned}\)
9000039001
Level:
C
Assuming \(x\in \mathbb{R}\),
find the solution set of the following system.
\[\begin{aligned}
- 4x & < -6 - 2x & &
\\2(x + 5) &\leq 16 & &
\end{aligned}\]
\(\emptyset \)
\((3;+\infty )\)
\((-\infty ;3)\)
\(\{3\}\)