"To solve the system of equations Zach isolated x^2 into the first equation and then substituted it into the second equation.What was the resulting equation
x^2 + y^2 = 25
x^2 / 16 - y^2 / 9 = 1
Answer:
[tex]81-25 y^{2}=0[/tex] is the resulting equation
Solution:
According to question,
To solve the given system of Equations Zach isolated [tex]x^2[/tex] from the first equation
Given first equation is:
[tex]x^{2}+y^{2}=25[/tex]
Separating [tex]x^2[/tex] term, we get
[tex]x^{2}=25-y^{2}[/tex] ------ eqn 1
And then substituted it into the second equation which is given below:-
[tex]\frac{x^{2}}{16}-\frac{y^{2}}{9}=1[/tex]
Substituting eqn 1 in above equation we get,
[tex]\frac{25-y^{2}}{16}-\frac{y^{2}}{9}=1[/tex]
[tex]9 \times\left(25-y^{2}\right)-16 y^{2}=144[/tex]
[tex]225-9 y^{2}-16 y^{2}=144[/tex]
[tex]81-25 y^{2}=0[/tex]
Which is the required equation
