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Answer:
Part ) The graph in the attached figure
Part b) The system has infinitely solutions
Step-by-step explanation:
Part a) Graph this system of inequalities
we have
y < -x+4 -----> inequality A
The solution of the inequality A is the shaded area below the dotted line
y=-x+4
The y-intercept of the dotted line is the point (0,4)
The x-intercept of the dotted line is the point (4,0)
The slope of the dotted line is negative (m=-1)
y > -x-2 -----> inequality B
The solution of the inequality B is the shaded area above the dotted line
y=-x-2
The y-intercept of the dotted line is the point (0,-2)
The x-intercept of the dotted line is the point (-2,0)
The slope of the dotted line is negative (m=-1)
using a graphing tool
The graph in the attached figure
Part b) How many solutions does this system of inequalities have?
we know that
The solution of the system of inequalities is the shaded area between the two dotted lines (see the attached figure)
therefore
The system has infinitely solutions
