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Solve the system of equations.

y=−x+2

3x+3y=6

Which best describes the solution?

(1 point)
Responses

One solution at (0,2).
One solution at open paren 0 comma 2 close paren .

One solution at (23,83).
One solution at open paren 2 thirds comma 8 thirds close paren .

There are infinitely many solutions.
There are infinitely many solutions.

There are no solutions.

1 answer

To solve the system of equations:

  1. Equation 1: \[ y = -x + 2 \]

  2. Equation 2: \[ 3x + 3y = 6 \] We can simplify Equation 2 by dividing all terms by 3: \[ x + y = 2 \]

Now we can rewrite Equation 2: \[ y = -x + 2 \]

Both equations are actually the same: \[ y = -x + 2 \]

This means that the two equations describe the same line.

Since both equations represent the same line, there are infinitely many solutions that lie on this line.

Thus, the correct answer is:

There are infinitely many solutions.