Questions: G2-T1 UNIT 6 LESSON 6 Equations inequalities Systems of Equations Systems of Equations Quick Check Solve the system of equations. y = -x + 2 3x + 3y = 6 Which best describes the solution? (1 point) One solution at (0,2) There are infinitely many solutions. There are no solutions. One solution at (2/3, 8/3)

Solution Steps

To solve the system of equations, we can use the substitution method. First, substitute the expression for \( y \) from the first equation into the second equation. Then, solve for \( x \). Once \( x \) is found, substitute it back into the first equation to find \( y \). Finally, check if the solution satisfies both equations to determine the correct description of the solution.

We start with the system of equations: \[ \begin{align_} y &= -x + 2 \quad (1) \\ 3x + 3y &= 6 \quad (2) \end{align_} \] Substituting equation (1) into equation (2): \[ 3x + 3(-x + 2) = 6 \]

Now, simplify the equation: \[ 3x - 3x + 6 = 6 \] This simplifies to: \[ 6 = 6 \] This is a true statement, indicating that the equations are dependent.

Since the equations are dependent, there are infinitely many solutions. The solutions can be expressed in terms of \( x \): \[ y = -x + 2 \] This means for any value of \( x \), there exists a corresponding \( y \).

Final Answer