Sure, let's break down the step-by-step solution for the system of equations given the conditions:
1. The sum of the two numbers is 84.
This can be formulated as the equation:
[tex]\[ x + y = 84 \][/tex]
So, solving for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], we get:
[tex]\[ y = 84 - x \][/tex]
2. The square of the first number is 6 more than the second number.
This can be expressed as the equation:
[tex]\[ x^2 = y + 6 \][/tex]
So, solving for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], we get:
[tex]\[ y = x^2 - 6 \][/tex]
Therefore, the system of equations is:
[tex]\[
\begin{array}{l}
y = -x + 84 \\
y = x^2 - 6
\end{array}
\][/tex]
