In the following exercises, which order pair are solution to the given equation

$x+3y=9$

(a)$(0,3)$(b)$(6,1)$(c)$(-3,-3)$

We are given an equation : $x+3y=9$and three coordinates : $(0,3),(6,1),$and$(-3,-3)$.

We need to find the solution of the given equation.

To check the first coordinate : $(0,3)$we need to put the value of $x$and $y$in the equation and see if L.H.S=R.H.S , here we know that $x=0$and $y=3$.

From the equation : $x+3y=9$the R.H.S is $9$, we need to solve L.H.S :

role="math" localid="1647199446308" $$\begin{gathered} x+3y=0+3\left(3\right) \\ =9 \end{gathered}$$

Therefore, L.H.S=R.H.S .

So, it is a solution of the given equation.

To check the second coordinate : $(6,1)$we need to put the value of $x$and $y$in the equation and see if L.H.S=R.H.S , here we know that $x=6$and $y=1$.

From the equation $x+3y=9$the R.H.S is $9$, we need to solve the L.H.S :

$$\begin{gathered} x+3y=6+3\left(1\right) \\ =9 \end{gathered}$$

Therefore, L.H.S=R.H.S

So, it is a solution of given equation.

To check the third coordinate : $(-3,-3)$we need to put the value of $x$and $y$in the equation and see if L.H.S=R.H.S .

Here, we know that $x=-3$and $y=-3$.

From the equation $x+3y=9$the R.H.S is $9$, we need to solve the L.H.S :

$$\begin{gathered} x+3y=-3+3(-3) \\ =-3-9 \\ =-12 \end{gathered}$$

Therefore, L.H.S is not equal to R.H.S .

So, it is not the solution of the given equation.