Systems of Equations Quick Check

Question

1 of 51 of 5 Items
Question
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 .

There are no solutions.
There are no solutions.

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

There are infinitely many solutions.

Answer 1

To solve the system of equations given:

1. \( y = -x + 2 \)
2. \( 3x + 3y = 6 \)

First, we can rearrange the second equation to see if it matches the form of the first equation.

Start with the second equation:

\( 3x + 3y = 6 \)

Divide everything by 3:

\( x + y = 2 \)

Now, we can express \( y \) in terms of \( x \):

\( y = -x + 2 \)

This equation is identical to the first equation. Therefore, both equations represent the same line.

Since both equations describe the same line, there are infinitely many solutions (any point on the line is a solution to both equations).

Thus, the best description of the solution is:

There are infinitely many solutions.