Determine the whole number unknowns for the solution set of the given graph of an inequality in two variables.
To determine the whole number unknowns for the solution set of the graph of an inequality in two variables, we need to identify the points on the graph that lie on the grid lines with integer values.
Consider the inequality $y \geq -2x + 3$, where $x$ and $y$ are whole numbers.
To find the whole number unknowns that satisfy this inequality, we can start by choosing some test points on the graph and checking if they satisfy the inequality.
Let's choose a few test points:
Point A: $x = 0, y = 0$
Plugging these values into the inequality, we get $0 \geq -2(0) + 3$ which simplifies to $0 \geq 3$. Since this is not true, Point A is not a solution.
Point B: $x = 1, y = 0$
Plugging these values into the inequality, we get $0 \geq -2(1) + 3$ which simplifies to $0 \geq 1$. Since this is not true, Point B is not a solution.
Point C: $x = 0, y = 1$
Plugging these values into the inequality, we get $1 \geq -2(0) + 3$ which simplifies to $1 \geq 3$. Since this is not true, Point C is not a solution.
Point D: $x = 1, y = 2$
Plugging these values into the inequality, we get $2 \geq -2(1) + 3$ which simplifies to $2 \geq 1$. This is true, so Point D is a solution.
Point E: $x = 2, y = 4$
Plugging these values into the inequality, we get $4 \geq -2(2) + 3$ which simplifies to $4 \geq -1$. This is true, so Point E is a solution.
Based on our test points, we have found two solutions: Point D (1, 2) and Point E (2, 4).
Therefore, the whole number unknowns for the solution set of the given graph are $x = 1$ and $y = 2$, as well as $x = 2$ and $y = 4$.