Determine which of the graphs is the graph of a system of inequalities with no solutions.(1 point)

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A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A solid line with arrows at both ends is plotted, and various regions of the graph are marked.
Image with alt text: A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A solid line with arrows at both ends is plotted, and various regions of the graph are marked.

A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.
Image with alt text: A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.

A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.
Image with alt text: A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 solid lines with arrows at both ends are plotted, and various regions of the graph are marked.

Two dashed lines and four points are graphed on a coordinate plane. The x-axis ranges from negative 6 to 30 in increments of 2. The y-axis ranges from negative 5 to 15 in increments of 1.
Image with alt text: Two dashed lines and four points are graphed on a coordinate plane. The x-axis ranges from negative 6 to 30 in increments of 2. The y-axis ranges from negative 5 to 15 in increments of 1.
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to choose answer say a b or c or d

Answer 1

To determine which graph represents a system of inequalities with no solutions, we need to identify a scenario where the regions defined by the inequalities do not intersect at all. This often happens when the lines represent constraints that define opposite regions.

Based on your description:

• The first option has one solid line, which indicates one single constraint, so it may have solutions.
• The second and third options describe systems with two solid lines; it's possible they might create a region of solutions depending on their orientation.
• The fourth option mentions two dashed lines and suggests more complexity in the arrangement.

Graphically, a system will have no solutions when the feasible regions defined by the inequalities do not overlap at all. This typically happens with parallel lines that open in opposite directions or when lines intersect and shade opposite regions.

Without seeing the graphs directly, I'd recommend you look for a graph where the shaded areas do not overlap at all. Typically, your best bet is with cases that clearly show parallel lines or configurations that indicate every possible solution is ruled out. Based on what you've described, the answer is likely option d, which shows two dashed lines and may indicate parallel constraints.

Please confirm with the specific graph details!