To find the solution to the given system of inequalities, we need to express each inequality in a standard form, usually in terms of \( y \).
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The first inequality is:
\(-3x + y \geq -4\)
We can rearrange this to solve for \( y \):
\[ y \geq 3x - 4 \] -
The second inequality is already in a suitable form:
\( y < -2x + 3 \)
Now, let's summarize the two inequalities:
- \( y \geq 3x - 4 \)
- \( y < -2x + 3 \)
The solution to the system of inequalities would be the area that satisfies both conditions on a graph. The solution is the region above the line \( y = 3x - 4 \) and below the line \( y = -2x + 3 \).
If you are looking for a single equation that represents this system, you would likely be asked for a statement of the solution, which provides the set of conditions rather than combining them into one equation.
If pressed to express it concisely, in the context of representing the regions defined by these inequalities, it could be described as:
- The solution set is defined by:
\[ { (x,y) \mid y \geq 3x - 4 \text{ and } y < -2x + 3 } \]
This means the area where both inequalities hold. However, it’s important to note that you can't just combine these inequalities into one standard equation, as they define a region in a two-dimensional space.