Questions: Solve by elimination: 7x + y = -9 -8x - y = 5 (-1,-2) (-2-1) (-2-3) (-8,-2)

Solution Steps

To solve the system of linear equations by elimination, we need to eliminate one of the variables by adding or subtracting the equations. Here, we can add the two equations to eliminate \( y \).

We start with the system of equations: \[ \begin{array}{l} 7x + y = -9 \quad (1) \\ -8x - y = 5 \quad (2) \end{array} \]

To eliminate \( y \), we can add equations (1) and (2): \[ (7x + y) + (-8x - y) = -9 + 5 \] This simplifies to: \[ -x = -4 \implies x = 4 \]

Now, we substitute \( x = 4 \) back into equation (1): \[ 7(4) + y = -9 \] This simplifies to: \[ 28 + y = -9 \implies y = -9 - 28 = -37 \]

Final Answer