The image shows two linear equations labeled $g$ and $h$:

• $g: y = -5x - 1$
• $h: y = -7x - 3$

To find the intersection point of these two lines, we solve the system of equations by setting $g = h$:

$-5x - 1 = -7x - 3$

Step-by-Step Solution:

1. Simplify the equation: $-5x + 7x = -3 + 1$ $2x = -2$

2. Solve for $x$: $x = -1$

3. Substitute $x = -1$ into either equation to find $y$. Using $g: y = -5x - 1$: $y = -5(-1) - 1$ $y = 5 - 1 = 4$

Intersection Point:

The intersection point is: $(x, y) = (-1, 4)$

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Related Questions:

1. What happens if the slopes of the two lines were equal?
2. How would you find the intersection point of a line and a parabola?
3. How can you determine whether two lines are parallel from their equations?
4. How do you verify that a point lies on a given line?
5. What is the geometric interpretation of this intersection point?

Tip:

Always check your solution by substituting the intersection point back into both equations!