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Alla [95]
3 years ago
8

Which of the following is a solution to the following system of inequalities?

Mathematics
1 answer:
iren2701 [21]3 years ago
4 0

Option D: (0,3) is the solution to the inequalities.

Explanation:

From the given graph, we can see that the equation of the inequalities are

$y>-x+1$ and $y\leq 2 x+3$

To determine the coordinate that satisfies the inequality, let us substitute the coordinates in both of the inequalities $y>-x+1$ and $y

Thus, we have,

Option A: (1,-1)

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$, we get,

y>-x+1\implies-1>0 is not true.

$y\leq 2 x+3 \implies -1\leq 5 is true.

Since, only one equation satisfies the condition, the coordinate (1,-1) is not a solution.

Hence, Option A is not the correct answer.

Option B: (-4,0)

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$, we get,

y>-x+1\implies0>5 is not true.

$y\leq 2 x+3 \implies 0\leq -5 is not true.

Since, both the equations does not satisfy the condition, the coordinate (-4,0) is not a solution.

Hence, Option B is not the correct answer.

Option C: (3,-2)

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$, we get,

y>-x+1\implies-2>-2 is not true.

$y\leq 2 x+3 \implies -2\leq 9 is true.

Since, only one equation satisfies the condition, the coordinate (3,-2) is not a solution.

Hence, Option C is not the correct answer.

Option D: (0,3)

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$, we get,

y>-x+1\implies3>1 is true.

$y\leq 2 x+3 \implies 3\leq 3 is true.

Since, both equation satisfies the condition, the coordinate (0,3) is a solution.

Hence, Option D is the correct answer.

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In general, solving for a particular variable involves "undoing" what has been done to the variable, usually in the reverse order. In part 4, the variable W has L added and the sum is multiplied by 2. We "undo" those operations, last operation first, by dividing by 2 and subtracting L.

The properties of equality say you can do what you like to an equation as long as you do the same thing to both sides of the equation. So, when we say "divide by 2", we mean "divide both sides of the equation by 2." Likewise, "subtract L" means "subtract L from both sides of the equation."

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