Questions: x + 2y = 6 3x - y = -10

Solution Steps

To solve the system of linear equations, we can use a method such as substitution or elimination. Here, we'll use the elimination method to eliminate one of the variables by adding or subtracting the equations. This will allow us to solve for one variable, and then substitute back to find the other variable.

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

1. & \quad x + 2y = 6 \\
2. & \quad 3x - y = -10 \end{align*} \]

From the first equation, we can express \( x \) in terms of \( y \): \[ x = 6 - 2y \]

Substituting \( x \) into the second equation: \[ 3(6 - 2y) - y = -10 \] Expanding this gives: \[ 18 - 6y - y = -10 \] Combining like terms results in: \[ 18 - 7y = -10 \] Solving for \( y \): \[ -7y = -10 - 18 \\ -7y = -28 \\ y = 4 \]

Now substituting \( y = 4 \) back into the expression for \( x \): \[ x = 6 - 2(4) \\ x = 6 - 8 \\ x = -2 \]

Final Answer