Question

Which statement is correct about the system of inequalities x+2/y < 1 and y−7 > 5?

• The set of all ordered pairs whose x-coordinate is in the interval (−∞,10) and whose y-coordinate is in (12,∞) is part of the complete solution for the system.

• The set of all ordered pairs whose x-coordinate is in the interval (−∞,10) and whose y-coordinate is in (5,∞) is part of the complete solution for the system.

• The set of all ordered pairs whose x-coordinate is in the interval (−∞,1) and whose y-coordinate is in (5,∞) is the complete solution for the system.

• The set of all ordered pairs whose x-coordinate is in the interval (10,∞) and whose y-coordinate is in (12,∞) is the complete solution for the system.

Answer 1

Given, the system of inequalities x+2/y < 1 and y−7 > 5.

Now, reducing the inequalities,

x+2/y<1 {This inequality denoted as red color.

xy-y<-2

y(x-1)<-2

we get, $x\in\ \R$ - {1}, and $y \in\ \R$ - {0}.

And, other inequality,

y−7 > 5 {This inequality denoted as blue color.

y>12

Here, we get, $y \in (12, \infty).$

Then, the common region of both the inequality are given by the over lapping of blue and red color i.e., $x \in (-\infty,1)\space and\space y \in (12, \infty).$

Therefore, graph of the given inequalities are,

Thus, NO option is correct.

Correct answer is

• The set of all ordered pairs whose x-coordinate is in the interval (-∞,1) and whose y-coordinate is in (12,∞) is the complete solution for the system.