1003020101
Level:
C
How many solutions has the inequality have in \( \mathbb{N}\times\mathbb{N} \)? (Hint: Solve the inequality graphically.)
\[ -4y\geq4x-8 \]
\( 1 \)
\( 4 \)
infinity
none
Systems of linear equations and inequalities
1003020304
Level:
A
Find the solution set of the equation
\[1-\left[4x+3\cdot(x-y)\right]=\frac{1-14x}2-\frac{3-6y}2\]
in \( \mathbb{R}\times\mathbb{R} \).
\( \emptyset \)
\( \left\{[x;y],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{\left[x;\frac13+x\right],x\in\mathbb{R}\right\} \)
\( \left\{\left[x;-\frac13\right],x\in\mathbb{R}\right\} \)
1003020303
Level:
A
Find the solution set of the equation
\[1-\frac{x-2y}4=x+\frac{y+2}2\]
in \( \mathbb{R}\times\mathbb{R} \).
\( \left\{[0;y],y\in\mathbb{R}\right\} \)
\( \left\{[x;y],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{\left[\frac{-4y}5;y\right],y\in\mathbb{R}\right\} \)
\( \{0\} \)
\( \emptyset \)
1003020302
Level:
A
Assuming \( [x;y]\in\mathbb{R}\times\mathbb{R} \), solve the equation
\[ x-y-\frac{x-y}2=\frac{x-y}3 \]
Decide which of the answers below does not express the set of roots.
\( \left\{[x;y],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{[x;x],x\in\mathbb{R}\right\} \)
\( \left\{[y;y],y\in\mathbb{R}\right\} \)
\( \left\{[t;t],t\in\mathbb{R}\right\} \)
1003020301
Level:
A
In \( \mathbb{R}\times\mathbb{R} \), find the solution set of the equation:
\[ 2x-\frac{x+2y}3=2+\frac83y \]
\( \left\{\left[2y+\frac65;y\right],y\in\mathbb{R}\right\} \)
\( \left\{\left[2y+\frac65;\frac x2-\frac35\right],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{\left[\frac{6+6y}5;y\right],y\in\mathbb{R}\right\} \)
\( \emptyset \)
9000039001
Level:
C
Assuming \(x\in \mathbb{R}\),
find the solution set of the following system.
\[\begin{aligned}
- 4x & < -6 - 2x & &
\\2(x + 5) &\leq 16 & &
\end{aligned}\]
\(\emptyset \)
\((3;+\infty )\)
\((-\infty ;3)\)
\(\{3\}\)
9000026001
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x +\phantom{ 3}y\leq &3 & &
\\y - 2x < & - 1 & &
\end{aligned}\]
blue
red
green
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9000026002
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x + y > &2 + x & &
\\y + 1\leq &x + 1 & &
\end{aligned}\]
green
red
yellow
blue
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
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blue
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