Question

Check whether the point \((-4, 3)\) lies on both the lines represented by the linear equations:
\(x + y + 1 = 0 \quad \text{and} \quad x - y = 1\)

Answer 1

For the first equation \(x + y + 1 = 0\): Substitute \(x = -4\) and \(y = 3\):

\[ (-4) + 3 + 1 = 0 \]

This is true, so the point lies on the first line.

For the second equation \(x - y = 1\): Substitute \(x = -4\) and \(y = 3\):

\[ (-4) - 3 = -7 \]

This is false, so the point does not lie on the second line.

Thus, the point \((-4, 3)\) lies on the first line but not on the second line.