Questions: Solve the following system by the elimination method -x-6y=1 -3x-4ixy=3

Transcript text: Solve the following system by the elimination method \[ \begin{array}{r} -x-6 y=1 \\ -3 x-4 i x y=3 \end{array} \]

Solution

Solution Steps

To solve the given system of linear equations using the elimination method, follow these steps:

Multiply the equations by suitable constants to align the coefficients of one of the variables.
Add or subtract the equations to eliminate one variable.
Solve for the remaining variable.
Substitute back to find the other variable.

Given system: \[ \begin{array}{r} -x - 6y = 1 \\ -3x - 4y = 3 \end{array} \]

Solution Approach

Multiply the first equation by 3 to align the coefficients of \(x\): \[ -3x - 18y = 3 \]
Subtract the second equation from the modified first equation to eliminate \(x\): \[ (-3x - 18y) - (-3x - 4y) = 3 - 3 \]
Solve for \(y\).
Substitute \(y\) back into one of the original equations to find \(x\).

Step 1: Align the Coefficients of \(x\)

Multiply the first equation by 3 to align the coefficients of \(x\): \[ -3x - 18y = 3 \]

Step 2: Eliminate \(x\)

Subtract the second equation from the modified first equation to eliminate \(x\): \[ (-3x - 18y) - (-3x - 4y) = 3 - 3 \] \[ -3x - 18y + 3x + 4y = 0 \] \[ -14y = 0 \] \[ y = 0 \]

Step 3: Solve for \(x\)

Substitute \(y = 0\) back into the first original equation: \[ -x - 6(0) = 1 \] \[ -x = 1 \] \[ x = -1 \]