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=(96)/(28)=(24)/(7)`

Substituting:

`y=-(24)/(7)+14`

Operating:

`y=(74)/(7)`

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