Determine whether the ordered pair is the solution to the system

$$\begin{gathered} 3x+y=0 \\ x+2y=-5 \end{gathered}$$

(a)$(1,-3)$

(b)$(0,0)$

The system of equations is

$$\begin{gathered} 3x+y=0 \\ x+2y=-5 \end{gathered}$$

Solutions to check are$(1,-3),(0,0)$

Plug $x=1,y=-3$into both equations and check whether left side is same as right side

First equation:

role="math" localid="1647532216764" $$\begin{gathered} 3\left(1\right)-3=0 \\ 3-3=0 \\ 0=0 \end{gathered}$$

Left side is equal to right side

So, $(1,-3)$is the solution for the first equation.

Second equation:

$$\begin{gathered} 1+2(-3)=-5 \\ 1-6=-5 \\ -5=-5 \end{gathered}$$

So, $(1,-3)$is the solution for the second equation.

Hence,

$(1,-3)$is the solution.

Plug $x=0,y=0$into both equations and check whether the left side is the same as the right side

First equation:

$$\begin{gathered} 3\left(0\right)+0=0 \\ 0+0=0 \\ 0=0 \end{gathered}$$

So,$(0,0)$is the solution of the first equation.

Second equation:

localid="1647532528247" $$\begin{gathered} 0+2\left(0\right)=-5 \\ 0+0=-5 \\ 0=-5 \end{gathered}$$

Left side is not same as right side.

So, $(0,0)$is not the solution for second equation.

Hence, $(0,0)$does not make both equation true.