Questions: -x-7y=-41 x-6y=-37

Transcript text: \[ \begin{array}{r} -x-7 y=-41 \\ x-6 y=-37 \end{array} \]

Solution

Solution Steps

To solve the system of linear equations, we can use the method of substitution or elimination. Here, we will use the elimination method to eliminate one of the variables and solve for the other.

Solution Approach

Add the two equations to eliminate \( x \).
Solve for \( y \).
Substitute the value of \( y \) back into one of the original equations to solve for \( x \).

Step 1: Set Up the System of Equations

We start with the given system of equations: \[ \begin{align_} -x - 7y &= -41 \quad (1) \\ x - 6y &= -37 \quad (2) \end{align_} \]

Step 2: Eliminate One Variable

To eliminate \( x \), we can add equations (1) and (2): \[ (-x - 7y) + (x - 6y) = -41 - 37 \] This simplifies to: \[ -13y = -78 \]

Step 3: Solve for \( y \)

Dividing both sides by -13 gives: \[ y = \frac{-78}{-13} = 6 \]

Step 4: Substitute \( y \) Back to Find \( x \)

Now, we substitute \( y = 6 \) back into equation (2): \[ x - 6(6) = -37 \] This simplifies to: \[ x - 36 = -37 \] Adding 36 to both sides results in: \[ x = -1 \]

Final Answer

The solution to the system of equations is: \[ \boxed{x = -1, \, y = 6} \]

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