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Maths-

General

Easy

Question

The solution to which system of inequalities is represented by the shaded region of the graph?

$y \leq 7$ , $y \leq 2 x + 1$
$y \leq 7$ , $y \geq 2 x + 1$
$x \leq 7$ , $2 y \leq x$
$x \leq 7$ , $2 y \geq x$

The correct answer is: $y less or equal than 7$ , $y less or equal than 2 x plus 1$

We use basic graph theory and logic to solve the problem.
Explanations:
Step 1 of 3:
We can observe that, in the graph, there is a line $y equals 7$ . The shaded region indicates below that line so the inequality showing the shaded region is given by, $y less or equal than 7$ …(i)
So, that narrows our choice of options to only A and B.
Step 2 of 3:
According to options A and B, the line is $y equals 2 x plus 1$ .
Now, the shaded region is left side of the line so, as $x$ decreases so $y$ decreases.
Hence the inequality satisfies this condition is given by, $y less or equal than 2 x plus 1$ …(ii)
Step 3 of 3:
Combining (i) and (ii), we have the system of inequalities as
$y less or equal than 7$ and $y less or equal than 2 x plus 1$
Final Answer:
The right option is— $y less or equal than 7$
$y less or equal than 2 x plus 1$

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