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: Check if the point \((-4, 3)\) satisfies the first equation:
We are given the first equation: \(x + y + 1 = 0\). Substituting \(x = -4\) and \(y = 3\) into the equation:
\[ -4 + 3 + 1 = 0 \] Simplifying the left-hand side:
\[ -4 + 3 + 1 = 0 \] Since the left-hand side equals the right-hand side, the point \((-4, 3)\) satisfies the first equation.

Step 2: Check if the point \((-4, 3)\) satisfies the second equation:
We are given the second equation: \(x - y = 1\). Substituting \(x = -4\) and \(y = 3\) into the equation:
\[ -4 - 3 = 1 \] Simplifying the left-hand side:
\[ -4 - 3 = -7 \] Since \(-7 \neq 1\), 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 does not satisfy the second equation \(x - y = 1\). Therefore, the point \((-4, 3)\) does not lie on both the lines.