Chapter 11, Problem 21CT

To determine

To find: The ordered pair form.

Answer to Problem 21CT

The solution in ordered triple form is $\left(1,3\right),\left(1,-3\right)$ .

Explanation of Solution

Given information:

The given equations are,

  $\left\{\begin{array}{c}3x^2+y^2=12\\ y^2=9x\end{array}\right\}$

Calculation:

Calculate the equations,

Divided both sides of the equation is $3x^2+9x=12$ by 3.

  $x^2+3x-4=0$

Calculate the value of $x$ .

  $\begin{array}{c}{x}^2-x+4x-4=0\\ x\left(x-1\right)+4\left(x-1\right)=0\\ \left(x+4\right)\left(x-1\right)=0\end{array}$

Apply zero-product rule.

  $\begin{array}{c}x+4=0\\ x=-4\end{array}$

Or,

  $\begin{array}{c}x-1=0\\ x=1\end{array}$

So we have $x=1$ .

Substitute the value of $x$ in the equation $y^2=9$ .

  $\begin{array}{l}{y}^2=9\left(1\right)\\ y=\pm 3\end{array}$

Therefore, the solution in ordered pair from is $\left(1,3\right),\left(1,-3\right)$ .