Questions: Use the elimination method to solve the system of equations. Choose the correct ordered pair. 7x + 3y = 30 -2x + 3y = 3 A. (6,5) B. (3,3) C. (3,5) D. (6,3)

Solution Steps

To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. Here, we can subtract the second equation from the first to eliminate \( y \). Then, we solve for \( x \) and substitute back to find \( y \).

We start with the system of equations: \[ \begin{align*}

1. & \quad 7x + 3y = 30 \\
2. & \quad -2x + 3y = 3 \end{align*} \]

To eliminate \( y \), we can subtract the second equation from the first: \[ (7x + 3y) - (-2x + 3y) = 30 - 3 \] This simplifies to: \[ 9x = 27 \]

Dividing both sides by 9 gives: \[ x = 3 \]

Now, we substitute \( x = 3 \) back into one of the original equations. Using the first equation: \[ 7(3) + 3y = 30 \] This simplifies to: \[ 21 + 3y = 30 \] Subtracting 21 from both sides results in: \[ 3y = 9 \] Dividing by 3 gives: \[ y = 3 \]

Final Answer