Mathematics, 02.08.2019 02:00 hisachokdee

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

Look at the graph below which part of the graph best represents the solution set to the system of in

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Answer from: Haleysaraya1

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 from: mia3128

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.

Look at the graph below which part of the graph best represents the solution set to the system of in

Answer from: Quest

Intinisbinidbifbisbe

Answer from: Quest

8y^50

step-by-step explanation:

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