Answer :
To solve the given system of equations:
[tex]\[ \left\{\begin{array}{l} x^2 + y^2 = 25 \\ \frac{x^2}{16} - \frac{y^2}{9} = 1 \end{array}\right. \][/tex]
we can isolate [tex]\(x^2\)[/tex] from the first equation and then substitute it into the second equation.
1. Start with the first equation:
[tex]\[ x^2 + y^2 = 25 \][/tex]
Isolate [tex]\(x^2\)[/tex] by subtracting [tex]\(y^2\)[/tex] from both sides:
[tex]\[ x^2 = 25 - y^2 \][/tex]
2. Substitute this expression for [tex]\(x^2\)[/tex] into the second equation:
[tex]\[ \frac{x^2}{16} - \frac{y^2}{9} = 1 \][/tex]
Substitute [tex]\(x^2 = 25 - y^2\)[/tex]:
[tex]\[ \frac{25 - y^2}{16} - \frac{y^2}{9} = 1 \][/tex]
Thus, the resulting equation is:
[tex]\[ \frac{25 - y^2}{16} - \frac{y^2}{9} = 1 \][/tex]
This corresponds to option B.
[tex]\[ \left\{\begin{array}{l} x^2 + y^2 = 25 \\ \frac{x^2}{16} - \frac{y^2}{9} = 1 \end{array}\right. \][/tex]
we can isolate [tex]\(x^2\)[/tex] from the first equation and then substitute it into the second equation.
1. Start with the first equation:
[tex]\[ x^2 + y^2 = 25 \][/tex]
Isolate [tex]\(x^2\)[/tex] by subtracting [tex]\(y^2\)[/tex] from both sides:
[tex]\[ x^2 = 25 - y^2 \][/tex]
2. Substitute this expression for [tex]\(x^2\)[/tex] into the second equation:
[tex]\[ \frac{x^2}{16} - \frac{y^2}{9} = 1 \][/tex]
Substitute [tex]\(x^2 = 25 - y^2\)[/tex]:
[tex]\[ \frac{25 - y^2}{16} - \frac{y^2}{9} = 1 \][/tex]
Thus, the resulting equation is:
[tex]\[ \frac{25 - y^2}{16} - \frac{y^2}{9} = 1 \][/tex]
This corresponds to option B.