Bring a large pot of cold water to a boil. Once boiled, season with salt and add in the linguine. Cook according to package directions, until tender. Drain and set off to the side.
Heat a large skillet over medium-high heat. Add in 1 tablespoon olive oil and minced garlic, if using. Add the shrimp and cook, stirring often, until the shrimp is pink and no longer opaque, about 5 to 7 minutes.
Transfer the shrimp to a plate and set aside. Return skillet to heat and add remaining 1 tablespoon olive oil. Add in the arugula, a handful at a time, and cook until wilted, about 5 minutes. Season with a bit of salt and pepper. Add back in the shrimp and stir in the pesto sauce. Cook for a few minutes to warm through. Taste and adjust seasoning accordingly.
Toss the shrimp and pesto with the cooked linguine noodles and cook for a few minutes to heat through. Serve and enjoy!