91Ó°ÊÓ

Consider the equation $3x-y=6$.

Check whether the points $\left(a\right)\left(3,3\right),\left(b\right)\left(2,0\right),\left(c\right)\left(4,-6\right)$are the solutions of the given equation or not.

The ordered pair is a solution of the given equation if the ordered pair satisfies the equation.

(a) Substitute $\left(x,y\right)=\left(3,3\right)$in $3x-y=6$.

$\begin{array}{rcl}3x-y& =& 6\\ 3\left(3\right)-3& =& 6\\ 9-6& =& 6\\ 6& =& 6\end{array}$

The ordered pair $\left(3,3\right)$satisfies the equation, because$6=6$is true.

So, the ordered pair is a solution to the given equation.

(b) Substitute $\left(x,y\right)=\left(2,0\right)$in $3x-y=6$.

$\begin{array}{rcl}3x-y& =& 6\\ 3\left(2\right)-0& =& 6\\ 6& =& 6\end{array}$

The ordered pair $\left(2,0\right)$satisfies the equation, becuase$6=6$is true.

So, the ordered pair is a solution to the given equation.

(c) Substitute $\left(4,-6\right)$for $\left(x,y\right)$in $3x-y=6$.

$\begin{array}{rcl}3x-y& =& 6\\ 3\left(4\right)-\left(-6\right)& =& 6\\ 12+6& =& 6\\ 18& =& 6\end{array}$

The ordered pair $\left(4,-6\right)$does not satifies the equation, because $18=6$is not true.

So, the ordered pair is not a solution to the given equation.