Answer :
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]
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]
