2. \( y=2 x \) 4. \( y-13 x=0 \) 6. \( x-y=0 \)

It looks like you've provided a list of equations. Let's analyze them one by one: 1. **Equation 1:** \( y = 2x \) This is a linear equation representing a line with a slope of 2 that passes through the origin (0,0). 2. **Equation 2:** \( y - 13x = 0 \) This can be rewritten as \( y = 13x \). This is another linear equation with a slope of 13, also passing through the origin. 3. **Equation 3:** \( x - y = 0 \) This can be rewritten as \( y = x \). This is a linear equation with a slope of 1, also passing through the origin. ### Finding Intersections To find the points of intersection between these lines, we can set the equations equal to each other. 1. **Intersection of \( y = 2x \) and \( y = 13x \):** \[ 2x = 13x \implies 0 = 11x \implies x = 0 \] Substituting \( x = 0 \) back into either equation gives \( y = 0 \). **Point of intersection:** \( (0, 0) \) 2. **Intersection of \( y = 2x \) and \( y = x \):** \[ 2x = x \implies 0 = -x \implies x = 0 \] Substituting \( x = 0 \) back into either equation gives \( y = 0 \). **Point of intersection:** \( (0, 0) \) 3. **Intersection of \( y = 13x \) and \( y = x \):** \[ 13x = x \implies 0 = 12x \implies x = 0 \] Substituting \( x = 0 \) back into either equation gives \( y = 0 \). **Point of intersection:** \( (0, 0) \) ### Summary All three lines intersect at the point \( (0, 0) \). If you have any specific questions or need further analysis, feel free to ask!