Question: Solve the system by graphing. 6x + 2y = -12 x - 2y = -2 Use the graphing tool to graph the…

Solve the system by graphing.

6x + 2y = -12 x - 2y = -2

Use the graphing tool to graph the system.

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Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The system has a single solution. The solution set is \((-2, 0)\).

B. There are infinitely many solutions and the equations are dependent. The solution set is \((x, y) | 6x + 2y = -12\).

Solution

To solve the system of equations: \[ \begin{cases} 6x + 2y = -12 & \\ x - 2y = -2 & \end{cases} \] First, add both equations to eliminate \( y \): \[ 6x + 2y + x - 2y = -12 + (-2) \] Simplifying the equation: \[ 7x = -14 & \] Solve for \( x \): \[ x = -2 & \] Next, substitute \( x = -2 \) into the second equation: \[ -2 - 2y = -2 & \] Solve for \( y \): \[ -2y = 0 & \] \[ y = 0 & \] Therefore, the solution to the system is \((-2, 0)\).