which graph shows the solution to the system of inequalities below? \\(\\begin{cases} x + y < 3 \\\\ -5x +…

Explanation:

Step1: Analyze ( x + y < 3 )

Rewrite as ( y < -x + 3 ). The line ( y = -x + 3 ) has a slope of (-1) and y - intercept ( 3 ). Since the inequality is ( < ), the line is dashed, and we shade below it.

Step2: Analyze ( -5x + 2y \leq 10 )

Rewrite as ( 2y \leq 5x + 10 ) or ( y \leq \frac{5}{2}x + 5 ). The line ( y=\frac{5}{2}x + 5 ) has a slope of ( \frac{5}{2} ) and y - intercept ( 5 ). Since the inequality is ( \leq ), the line is solid, and we shade below it.

Step3: Check the graph

The given graph has a solid line (for ( -5x + 2y \leq 10 )) with y - intercept ( 5 ) and a dashed line (for ( x + y < 3 )) with y - intercept ( 3 ). The shaded region is the intersection of the regions below ( y < -x + 3 ) and below ( y \leq \frac{5}{2}x + 5 ), which matches the solution of the system.

Answer:

The graph shown (the one with the dashed line ( x + y = 3 ), solid line ( - 5x+2y = 10 ), and the shaded region as in the provided image) is the solution graph.