Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
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.
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.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.