Question

How do I identify coefficients in the linear equation 8x−3y=2x+9y?

Answer 1

To identify the coefficients in the linear equation \(8x - 3y = 2x + 9y\), you need to rearrange the equation into the standard form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are constants.

1. Start with the given equation:
\[
8x - 3y = 2x + 9y
\]

2. Move all terms involving \(x\) and \(y\) to one side of the equation. Subtract \(2x\) and \(9y\) from both sides:
\[
8x - 2x - 3y - 9y = 0
\]

3. Simplify the left side:
\[
(8x - 2x) + (-3y - 9y) = 0 \implies 6x - 12y = 0
\]

4. This gives us the equation in standard form:
\[
6x - 12y = 0
\]

From this equation, we can identify the coefficients:
- The coefficient of \(x\) (\(A\)) is \(6\).
- The coefficient of \(y\) (\(B\)) is \(-12\).
- The constant term (\(C\)) is \(0\).

So, the coefficients are:
- \(A = 6\)
- \(B = -12\)
- \(C = 0\)