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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]
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