Graph the solution of the following system. Find the vertices of the solution. {:[y = 3],[x

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Graph the solution of the following system. Find the vertices of the solution.  {:[y <= x],[x+y >= 3],[x <= 7]:}

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Graph Inequality y <= x: Graph the first inequality y <= x. To graph y <= x, first graph the line y = x. This is a straight line that passes through the origin (0,0) and has a slope of 1, meaning it makes a 45-degree angle with the x-axis. Since the inequality is less than or equal to, we will shade the region below the line.Graph Inequality x + y >= 3: Graph the second inequality x + y >= 3. To graph x + y >= 3, first graph the line x + y = 3. This line intersects the y-axis at (0,3) and the x-axis at (3,0). Since the inequality is greater than or equal to, we will shade the region above the line.Graph Inequality x <= 7: Graph the third inequality x <= 7. To graph x <= 7, first graph the vertical line x = 7. This line is parallel to the y-axis and passes through the point (7,0) on the x-axis. Since the inequality is less than or equal to, we will shade the region to the left of the line.Find Intersection Region: Find the intersection region. The solution to the system of inequalities is the region where all the shaded areas overlap. This region is a polygon, and we need to find its vertices.Find Polygon Vertices: Find the vertices of the polygon. The vertices of the polygon are the points of intersection of the lines y = x, x + y = 3, and x = 7. We find these points by solving the equations two at a time. First, find the intersection of y = x and x + y = 3: x = y x + y = 3 Substitute x for y in the second equation: x + x = 3 2x = 3 x = 3/2 y = x = 3/2 So, one vertex is at (3/2, 3/2).Find Vertex 1: Find the intersection of x + y = 3 and x = 7: x + y = 3 x = 7 Substitute x = 7 into the first equation: 7 + y = 3 y = 3 - 7 y = -4 So, another vertex is at (7, -4).Find Vertex 2: Find the intersection of y = x and x = 7: y = x x = 7 Substitute x = 7 into the first equation: y = 7 So, the third vertex is at (7, 7).Find Vertex 3: Check if there are any more vertices. We have found the vertices where the lines intersect, but we also need to check the points where the lines intersect the axes. The line x + y = 3 intersects the y-axis at (0,3) and the x-axis at (3,0). The line y = x intersects the axes at (0,0). The line x = 7 intersects the y-axis above the point (0,3), so it does not provide an additional vertex. Therefore, we have all the vertices of the polygon.

Graph the solution of the following system. Find the vertices of the solution. $\newline$ $\begin{cases} y \leq x \ x+y \geq 3 \ x \leq 7 \end{cases}$

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Graph the solution of the following system. Find the vertices of the solution.\newline{y≤x x+y≥3 x≤7\begin{cases} y \leq x \ x+y \geq 3 \ x \leq 7 \end{cases}{y≤x x+y≥3 x≤7​

Graph the solution of the following system. Find the vertices of the solution. $\newline$ $\begin{cases} y \leq x \ x+y \geq 3 \ x \leq 7 \end{cases}$