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: Test the first equation

Given the equation \( x + y + 1 = 0 \). To determine if the point \( (-4, 3) \) satisfies this equation, substitute \( x = -4 \) and \( y = 3 \):
\[ (-4) + 3 + 1 = 0 \] Simplify the expression:
\[ -4 + 3 + 1 = 0 \] \[ 0 = 0 \] The equality holds true, confirming that the point \( (-4, 3) \) is on the first line.

Step 2: Test the second equation

Now, evaluate if the point \( (-4, 3) \) lies on the second line, represented by the equation \( x - y = 1 \). Substitute \( x = -4 \) and \( y = 3 \):
\[ (-4) - 3 = -7 \] As \( -7 eq 1 \), the equation is not satisfied. Therefore, the point does not lie on the second line.

Step 3: Final determination

Consequently, the point \( (-4, 3) \) is located on the first line but not on the second line.