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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 :

GinnyAnsweridn
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]
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