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Which of the following systems of linear inequalities is represented by thesolution graphed below?

Which of the following systems of linear inequalities is represented by thesolution-example-1
User Machisuji
by
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1 Answer

27 votes
27 votes

We are given the graph of the solution of a system of inequalities. To determine the inequality associated to this we will first determine the equation of the line that represents the boundary of the solution. We notice that the graph passes through the origin, therefore, the y-intercept is zero and the general form of the graph is:


y=mx

We also notice that the point:


(x,y)=(1,1)

Plugging in the values we get:


\begin{gathered} 1=m(1) \\ 1=m \end{gathered}

Therefore, the equation of the line is:


y=x

In the graph, we notice that the line is included in the solution and that the solution is the point above the line, therefore, one of the inequalities of the system is:


y\ge x

The other line is a horizontal line, and therefore, it must have the form:


y=k

Where "k" is the y-intercept, in this case, y = 2.

Since the solution is the points beneath the horizontal line and since the line appears with a dotted line this means that the solution is the point that are smaller than the line without including the line, like this:


y<2

Therefore, the right answer is A.

User Pllx
by
2.5k points
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