Question

Determine if the ordered pair provided is a solution to the linear system:3x+7y=1 and 2x+4y=0; (2,3) The system has no solution as the lines are parallel. The ordered pair (2, 3) is not a solution to the system. Yes, (2, 3) is a solution to the system. The system has no solution as the lines are perpendicular.

Answer 1

The correct answer is:

The ordered pair (2, 3) is not a solution to the system.

Step-by-step explanation:

The system given is:

`\begin{cases}3x+7y={1} \\ 2x+4y={0}\end{cases}`

If (2, 3) is a solution of the system, then replacing x = 2 and y = 3 on both equations should give a correct result and the same on both equatiions.

In the first equation;

`\begin{gathered} 3\cdot2+7\cdot3=1 \\ 6+21=1 \\ 27=1 \end{gathered}`

We can see that this result is not true, as 27 is not equal to 1.

In the second equation:

`\begin{gathered} 2\cdot2+4\cdot3=0 \\ 4+12=0 \\ 16=0 \end{gathered}`

Once again, a false result.

To see in the system has equations, let's solve for x in the second equation:

`\begin{gathered} 2x+4y=0 \\ 2x=-4y \\ x=-2y \end{gathered}`

Now, we can use substitution in the first equation:

`3(-2y)+7y=1`

And solve for y:

`\begin{gathered} -6y+7y=1 \\ y=1 \end{gathered}`

Now, we can find the value of x:

`x=-2\cdot1=-2`

The solution to the system is (-2, 1)

Thus, the correct option is "The ordered pair (2, 3) is not a solution to the system"