Question

Look at the graph below Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≥ −1

Answer 1

ANSWER

Part A

EXPLANATION

The given inequalities are,

$y \geqslant x + 1$

and

$y + x \geqslant - 1$

To see which part of the graph best represent the solution set, choose a point from each part and substitute in to the inequalities.

If a point from a given part satisfies the inequalities simultaneously, then that part best represents the solution set.

Part A.

We choose
$(0,2)$
We plug in to the inequalities.

$2 \geqslant 0 + 1$

$\Rightarrow \: 2 \geqslant 1$
The above inequality is true.

We plug in to the second inequality.

$2 + 0 \geqslant - 1$

.
$\Rightarrow \: 2 \geqslant - 1$

This statement is also true.

Part B.

If we plug in
$(-2,0)$
in to the first statement, we get,

$0 \geqslant - 2 + 1$

This implies that,

$0 \geqslant - 1$

This is true.

If substitute in to the second, we get,

$0 + - 2\geqslant - 1$

$\Rightarrow \: - 2 \geqslant - 1$
This is false.

Part C

We plug
$(0,-2)$
in to the first inequality

$- 2 \geqslant 0 + 1$
This means that,

$- 2 \geqslant 1$
This is false.

We plug in to the second inequality,

$- 2 + 0 \geqslant -1$

$- 2 \geqslant -1$

False.

Part D also has the point

$(2,0)$

We put this point in to the first inequality to get,

$0 \geqslant 2 + 1$
$0 \geqslant 3$
This is false.

Then in to the second inequality.

$0 + 2 \geqslant 1$
$2 \geqslant -1$

This final statement is true.

Since the point from Part A satisfies both inequalities simultaneously, it represents the solution set.

Answer 2

Answer:

The solution set of given inequalities are represented by Part A.

Step-by-step explanation:

The given inequalities are

$y\geq x+1$

$y+x\geq -1$

The related equations of both inequalities are

$y=x+1$

Put x=0, to find the y-intercept and put y=0, to find x intercept.

$y=0+1\Rightarrow y=1$

$0=x+1\Rightarrow x=-1$

Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,1).

Similarly, for the second related equation

$y+x=-1$

$y+0=-1\Rightarrow y=-1$

$0+x=-1\Rightarrow x=-1$

Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).

Now, join the x and y-intercepts of both lines to draw the line.

Now check the given inequalities by (0,0).

$0\geq 0+1\Rightarrow 0\geq 1$

It is a false statement, therefore the shaded region is in the opposite side of origin.

$0+0\geq -1\Rightarrow 0\geq -1$

It is a true statement, therefore the shaded region is about the origin.

From the below figure we can say that the solution set of given inequalities are represented by Part A.