sweetnessnbab
Answered

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The point [tex]$(0,0)$[/tex] is a solution to which of these inequalities?

A. [tex]y + 4 \ \textless \ 3x + 1[/tex]

B. [tex]y - 1 \ \textless \ 3x - 4[/tex]

C. [tex]y - 4 \ \textless \ 3x - 1[/tex]

D. [tex]y + 4 \ \textless \ 3x - 1[/tex]

Sagot :

GinnyAnswer
To determine which of the given inequalities the point \((0,0)\) is a solution, we need to substitute \(x = 0\) and \(y = 0\) into each inequality and check if the resulting statements are true. Let's evaluate each inequality one by one:

Inequality A: \(y + 4 < 3x + 1\)

Substitute \(x = 0\) and \(y = 0\):
[tex]\[ 0 + 4 < 3(0) + 1 \][/tex]
[tex]\[ 4 < 1 \][/tex]

This statement is False.

Inequality B: \(y - 1 < 3x - 4\)

Substitute \(x = 0\) and \(y = 0\):
[tex]\[ 0 - 1 < 3(0) - 4 \][/tex]
[tex]\[ -1 < -4 \][/tex]

This statement is False.

Inequality C: \(y - 4 < 3x - 1\)

Substitute \(x = 0\) and \(y = 0\):
[tex]\[ 0 - 4 < 3(0) - 1 \][/tex]
[tex]\[ -4 < -1 \][/tex]

This statement is True.

Inequality D: \(y + 4 < 3x - 1\)

Substitute \(x = 0\) and \(y = 0\):
[tex]\[ 0 + 4 < 3(0) - 1 \][/tex]
[tex]\[ 4 < -1 \][/tex]

This statement is False.

So, the point \((0,0)\) is a solution only to inequality:

C. [tex]\(y - 4 < 3x - 1\)[/tex]
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