Answered

Which statement is true about the system x-3y=2 and y=x+6?

1. (8, 2) is not a solution to either equation, so it is not a solution to the system.

2. (8, 2) is a solution to one equation but not the other one, so it is a solution to the system.

3. (8,2) is a solution to both equations, so it is a solution to the system.

4. (8, 2) is a solution to one equation but not the other one, so it is not a solution to the system.

Answer :

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The true statement about the system of equations is the fourth one:

"(8, 2) is a solution to one equation but not the other one, so it is not a solution to the system."

Which statement is true about the system?

The system of equations is:

x - 3y = 2

y = x + 6

We want to see which statement is true, all of them refer to the point (8, 2), so let's see if it is a solution of the system.

Replacing the values in the first equation we will get:

8 - 3*2 = 2

8 - 6  =2

2 = 2

For the second equation:

2 =8 + 6

2 = 14

This is false, so (8, 2) is not a solution of the second equation.

Then the true statement is:

" (8, 2) is a solution to one equation but not the other one, so it is not a solution to the system."

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