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

Step 1: Verify the point \((-4, 3)\) against the first equation.
The first equation is \(x + y + 1 = 0\). Substitute \(x = -4\) and \(y = 3\):
\[ -4 + 3 + 1 = 0 \] The left side simplifies to:
\[ 0 = 0 \] The point \((-4, 3)\) satisfies the first equation.

Step 2: Verify the point \((-4, 3)\) against the second equation.
The second equation is \(x - y = 1\). Substitute \(x = -4\) and \(y = 3\):
\[ -4 - 3 = 1 \] The left side simplifies to:
\[ -7 = 1 \] Since \(-7 eq 1\), the point \((-4, 3)\) does not satisfy the second equation.

Step 3: Conclusion.
The point \((-4, 3)\) satisfies the first equation \(x + y + 1 = 0\) but not the second equation \(x - y = 1\). Consequently, the point \((-4, 3)\) does not lie on both lines.