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Determine whether the ordered pair [tex]\((3, 10)\)[/tex] is a solution of the given system:

[tex]\[
\begin{array}{l}
y \ \textgreater \ 2x + 1 \\
y \ \textless \ 3x + 7
\end{array}
\][/tex]

Is [tex]\((3, 10)\)[/tex] a solution of the given system?

A. No

B. Yes



Answer :

GinnyAnswer
To determine if the ordered pair (3, 10) is a solution to the given system of inequalities, we will substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 10 \)[/tex] into each inequality and check if both are satisfied.

The given system of inequalities is:
1. [tex]\( y > 2x + 1 \)[/tex]
2. [tex]\( y < 3x + 7 \)[/tex]

Step 1: Check the first inequality [tex]\( y > 2x + 1 \)[/tex]:

Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 10 \)[/tex] into the inequality:
[tex]\[ 10 > 2(3) + 1 \][/tex]

Calculate the right-hand side:
[tex]\[ 10 > 6 + 1 \][/tex]
[tex]\[ 10 > 7 \][/tex]

This inequality is true.

Step 2: Check the second inequality [tex]\( y < 3x + 7 \)[/tex]:

Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 10 \)[/tex] into the inequality:
[tex]\[ 10 < 3(3) + 7 \][/tex]

Calculate the right-hand side:
[tex]\[ 10 < 9 + 7 \][/tex]
[tex]\[ 10 < 16 \][/tex]

This inequality is also true.

Since both inequalities are satisfied, the ordered pair [tex]\( (3, 10) \)[/tex] is a solution to the given system of inequalities.

Therefore, the answer is:
Yes, (3, 10) is a solution of the given system.

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