1. \( y=x^{2}-5 x+1 \) 2. \( 3 x+y-3=0 \) 3. \( y(y)=3 x+y+1 \) 4. \( y+x^{2}=2 x^{2}-4 x-1 \) 3. \( y-2=x^{2}-2 \)

It looks like you've provided a list of equations involving \(x\) and \(y\). Let's analyze each equation one by one. 1. **Equation 1**: \( y = x^2 - 5x + 1 \) This is a quadratic equation in terms of \(x\). It represents a parabola that opens upwards. 2. **Equation 2**: \( 3x + y - 3 = 0 \) This can be rearranged to \( y = -3x + 3 \). This is a linear equation representing a straight line with a slope of -3. 3. **Equation 3**: \( y(y) = 3x + y + 1 \) This equation seems to have a typo. If you meant \( y = 3x + y + 1 \), it simplifies to \( 0 = 3x + 1 \), which is not dependent on \(y\). Please clarify this equation. 4. **Equation 4**: \( y + x^2 = 2x^2 - 4x - 1 \) Rearranging gives \( y = 2x^2 - 4x - 1 - x^2 = x^2 - 4x - 1 \). This is another quadratic equation in terms of \(x\). 5. **Equation 5**: \( y - 2 = x^2 - 2 \) Rearranging gives \( y = x^2 + 0 = x^2 \). This is a simple quadratic equation representing a parabola that opens upwards. If you need to solve these equations or find intersections, please specify which equations you would like to work with or what specific information you are looking for!