Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Type the correct answer in each box. Use numerals instead of words.

The sum of two numbers is 84. The square of the first number is 6 more than the second number. Write a system of equations to find the value of [tex]\( x \)[/tex], the first number, and [tex]\( y \)[/tex], the second number.

[tex]\[
\begin{array}{l}
y = -x + \square \\
y = x^2 + \square
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To find the values of the numbers given that their sum is 84 and the square of the first number is 6 more than the second number, we can establish the following system of equations:

1. Given the sum of the numbers:
[tex]\[ x + y = 84 \][/tex]
We can solve for [tex]\( y \)[/tex]:
[tex]\[ y = 84 - x \][/tex]

So the first equation in the system is:
[tex]\[ y = -x + 84 \][/tex]

2. Given that the square of the first number is 6 more than the second number:
[tex]\[ x^2 = y + 6 \][/tex]
Again, solving for [tex]\( y \)[/tex]:
[tex]\[ y = x^2 - 6 \][/tex]

So the second equation in the system is:
[tex]\[ y = x^2 - 6 \][/tex]

Hence, the system of equations is:
[tex]\[ \begin{array}{l} y = -x + 84 \\ y = x^2 - 6 \end{array} \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.