Question

linear equations, inequalities, and systems section f checkpoint
1 draw a graph of a system of inequalities that has no solution.
standard
a - rei.d.12: ___

Explanation:

Step1: Pick parallel boundary lines

Choose two parallel lines, e.g., $y = x + 2$ and $y = x - 1$.

Step2: Define conflicting inequalities

Set inequalities: $y > x + 2$ and $y < x - 1$.

Step3: Graph boundary lines

Draw $y = x + 2$ (dashed, slope=1, y-int=2) and $y = x - 1$ (dashed, slope=1, y-int=-1).

Step4: Shade solution regions

Shade above $y = x + 2$, shade below $y = x - 1$. No overlapping shaded area.

Answer:

A system like $\boldsymbol{y > x + 2}$ and $\boldsymbol{y < x - 1}$ has no solution. When graphed, the dashed parallel boundary lines and non-overlapping shaded regions show there is no point that satisfies both inequalities.