Question

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Answer 1

Answer:

Here, the given system of inequalities,

y ≤ -x + 55       --------(1)

y > -1.5 x + 15  -------(2),

The related line of the inequality (1) is,

y = - x + 55 ------(3)

Which having x-intercept = (55,0)

And, y-intercept = (0,55),

Also, at (0,0),

Inequality (1), 0 ≤ 0 + 55 ( True )

Thus, it will contain the origin,

Also, ≤ sign stated that the inequality (1) is a solid line,

Now, The related line of the inequality (2) is,

y =  -1.5 x + 15 -----(3)

Which having x-intercept = (10,0)

And, y-intercept = (0,15),

Also, at (0,0),

Inequality (1), 0 > 0 + 15 ( False )

Thus, it will not contain the origin,

Also, > sign stated that the inequality (2) is a dashed line,

Now after solving equation (3) and (4) we get,

x = -80 and y = 135

⇒ The intersection point of line (3) and (4) is (-80,135)

Hence, by the above explanation we can plot the given system of inequalities ( Shown below )