Problem
Determine whether or not the equation is a linear equation in two variables. \[ 5 x-y^{2}=1 \] Only use the numbers from the given linear equation. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. Yes, the given equation is a linear equation in two variables. It can be written in the form $\mathrm{Ax}+\mathrm{By}=\mathrm{C}$ where $\mathrm{A}=\square, \mathrm{B}=\square$, and $\mathrm{C}=\square$. B. No, the given equation is not a linear equation in two variables. It cannot be written in the form $A x+B y=C$.
Solution
Step 1 ：A linear equation in two variables is of the form Ax + By = C, where A, B, and C are constants, and x and y are variables.
Step 2 ：The given equation is 5x - y^2 = 1.
Step 3 ：This equation is not in the form Ax + By = C because of the y^2 term.
Step 4 ：Therefore, the given equation is not a linear equation in two variables.
Step 5 ：\(\boxed{\text{B. No, the given equation is not a linear equation in two variables. It cannot be written in the form } Ax + By = C}\)
