Graph the solution of the following system of inequalities. Find the vertex of the solution. {:[x+y = 9]:}

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Graph the solution of the following system of inequalities. Find the vertex of the solution.  {:[x+y <= 7],[3x-y >= 9]:}

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Graph Inequality x + y <= 7: Graph the first inequality x + y <= 7. To graph this inequality, first graph the line x + y = 7. This is a straight line with a slope of -1 (since y = -x + 7) and a y-intercept of 7. To find another point, set x to 0, then y = 7. Set y to 0, then x = 7. Plot these points (0,7) and (7,0) and draw a line through them. Since the inequality is less than or equal to, shade the area below the line.Graph Inequality 3x - y >= 9: Graph the second inequality 3x - y >= 9. To graph this inequality, first graph the line 3x - y = 9. This is a straight line with a slope of 3 (since y = 3x - 9) and a y-intercept of -9. To find another point, set x to 0, then y = -9. Set y to 0, then x = 3. Plot these points (0,-9) and (3,0) and draw a line through them. Since the inequality is greater than or equal to, shade the area above the line.Identify Overlapping Region: Identify the region where the shaded areas from Step 1 and Step 2 overlap. The solution to the system of inequalities is the region where both shaded areas overlap. This is the feasible region that satisfies both inequalities.Find Solution Vertex: Find the vertex of the solution. The vertex of the solution is the point of intersection of the two lines x + y = 7 and 3x - y = 9. To find this point, we can solve the system of equations simultaneously. x + y = 7 3x - y = 9 Adding these two equations, we get: 4x = 16 x = 4 Substitute x = 4 into the first equation: 4 + y = 7 y = 3 So the vertex of the solution is at the point (4, 3).

Graph the solution of the following system of inequalities. Find the vertex of the solution. $\newline$ $\begin{cases} x+y \leq 7 \ 3x-y \geq 9 \end{cases}$

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Graph the solution of the following system of inequalities. Find the vertex of the solution.\newline{x+y≤7 3x−y≥9\begin{cases} x+y \leq 7 \ 3x-y \geq 9 \end{cases}{x+y≤7 3x−y≥9​

Graph the solution of the following system of inequalities. Find the vertex of the solution. $\newline$ $\begin{cases} x+y \leq 7 \ 3x-y \geq 9 \end{cases}$