Question

solve the system using any method. explain your choice of method

Answer 1

Solve the system of equations.

$\begin{gathered} -x^2+y^2=100 \\ y=-x+14 \end{gathered}$

I will choose the method of substitution, i.e., solve for one of the variables in the second equation and substitute it into the first equation.

I didn't use the elimination method because the variables are squared in the first equation and not in the second.

Substituting y into the first equation:

$-x^2+(-x+14)^2=100$

Operating:

$-x^2+x^2-28x+196^{}=100$

Simplifying:

$-28x=-96$

Dividing by -28 and simplifying:

$x=\frac{96}{28}=\frac{24}{7}$

Substituting:

$y=-\frac{24}{7}+14$

Operating:

$y=\frac{74}{7}$

Answer: x = 24/7 , y = 74/7