Systems of inequalities (basic graph-based problems) — Heart of Algebra

Questions in this quiz (5)

1. Which of the following ordered pairs is a solution to the system:$$y\leq2x+3$$$$y$$ > $$-x+1$$

   • $$(0,0)$$
   • $$(1,4)$$
   • $$(2,-1)$$
   • $$(-1,0)$$

2. The system $$y\le-2x+6$$ and $$y$$ > $$0$$ represents a region that lies:

   • above both lines
   • below both lines
   • below one line and above the $$x$$-axis
   • below one line and below the $$x$$-axis

3. If the shaded region of a graph includes the point $$(2,1)$$ and excludes $$(0,4)$$, which of the following could represent the system?

   • $$y$$ > $$x$$ and $$y$$ < $$2x-1$$
   • $$y$$ > $$x$$ and $$y$$ > $$2x-1$$
   • $$y$$ < $$x$$ and $$y$$ < $$2x-1$$
   • $$y$$<$$ x$$ and $$y$$ > $$2x-1$$

4. The solution set of $$y$$ > $$-\frac12x+2$$ and $$y\le x+1$$ is best described as:

   • the region above both lines
   • the region below both lines
   • the region between the two lines
   • not known

5. Which inequality describes the shaded region below the line $$y=\frac{3}{4}x+1$$?

   • $$y$$ > $$\frac{3}{4}x+1$$
   • $$y$$ < $$\frac{3}{4}x+1$$
   • $$y\ge\frac{3}{4}x+1$$
   • $$y\le\frac{3}{4}x+1$$