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: Substituting values into the first equation:

We are given the equation \( x + y + 1 = 0 \). To check if the point \( (-4, 3) \) lies on this line, substitute \( x = -4 \) and \( y = 3 \) into the equation:
\[ (-4) + 3 + 1 = 0 \] Simplifying: \[ -4 + 3 + 1 = 0 \] \[ 0 = 0 \] Since this is true, the point \( (-4, 3) \) lies on the first line.

Step 2: Substituting values into the second equation:

Next, we check if the point \( (-4, 3) \) lies on the second line given by the equation \( x - y = 1 \). Substitute \( x = -4 \) and \( y = 3 \) into this equation:
\[ (-4) - 3 = -7 \] Since \( -7 \neq 1 \), the equation is false, and therefore the point does not lie on the second line.

Step 3: Conclusion:

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