Problem: Article: Linear equations have distinct components. The variable is the symbol (usually a letter like x or y) for a number you do not yet know. The constant is a number that remains consistent. The coefficient is a number before a variable, which is used to multiply it. For example, in the linear equation 2x + 4y = 8, x and y are variables. The constant is 8. The numbers 2 and 4 are coefficients. A system of equations with two variables can be written as follows:ax + by = pcx + dy = qAny of the constants (p, q) can be zero, with the exception that each equation must have at least one variable (x, y) in it. When you have a linear system, you can use a matrix to rewrite it, then use the algebraic properties of that matrix to solve it. To rewrite a linear system, you use A to represent the coefficients matrix, C to represent the constants matrix, and X to represent the unknown matrix. The linear system above, for example, can be rewritten as a matrix equation as follows: A x X = C. An augmented matrix is a matrix obtained by appending columns of two matrices. If you have two matrices, A and C, which looks like this:You can create an augmented matrix by putting them together. The augmented matrix would look like this: For example, consider the following linear system:2x + 4y = 8x + y = 2Your augmented matrix would be a 2x3 matrix that looks like this:
Summary: Know your terminology. Recognize the form for a system of equations. Understand matrix equations. Understand augmented matrices.

INPUT ARTICLE: Article: If your dog or cat was the one responsible for the bite, enroll in a training program or work with your pet at home to teach it not to bite. Often, many animal rescues and shelters have training programs for aggressive pets. Call and ask if their programs are open to pets from the community, as well.  If you have a pet that is not easily trained, such as a snake, frog, or small mammal, make sure the pet is kept in proper housing with an effective locking mechanism. If you have a pet that requires certain equipment such as gloves to handle them, make sure to always use the equipment properly every time you handle your pet. Different types of animals have different signs that indicate they may be about to bite. Learn common signs of distress for typical pets such as dogs and cats to help identify potential bite risks.  Signs a dog is about to bite may include snarling, barking, growling, ears back, an aggressively wagging tail, repeated stress yawning, and more.  Signs a cat is about to bite or scratch include increased stiffness in the body and a twitching of the tail. Cats are especially prone to bite during tummy rubs, as well. If you do not know if a pet is friendly or not, err on the side of caution. Keep a safe distance from any pets you do not know until you’ve talked to their owners and have a better idea of the pet’s demeanour.  When you want to approach a new pet for the first time, ask the owner, “Is it alright if I touch your pet? Does your pet have any issues with temperament that I should be aware of while interacting with them?” Allow the pet owner to instruct you or demonstrate for you how to interact with their pet for the first time.

SUMMARY: Teach your pet not to bite. Know the signs of an impending bite. Stay away from unfamiliar pets.

In one sentence, describe what the following article is about: Make a deal with your parents. Tell them that if they drive you to the store, you will wash the dishes after dinner. Since they are taking time out of their day to drive you, offer to do something that will give them one less thing to do that day. Offer to do the favors ahead of time. If you want them to drive you to the dance Friday night, offer to do laundry on Thursday so they know your word is good. It might not hurt to butter your parents up a little bit. Clean your room, complete your homework, or vacuum before you ask them for a ride. This might help you get on their good side and show them that you really want to go. By completing chores and schoolwork before asking, you put yourself at an advantage. If you ask your parents to drive you somewhere and they ask, "Is your homework done?" or "Have you cleaned your room?", you can say yes. If the gas money is an issue, offer to pay for the gas. Use your allowance or money from your paper route to cover it. This shows you are responsible and willing to share some of the responsibility for the ride. Don't offer to pay them for the ride. This might be seen as a bribe or make them feel like a taxi service, which is not what you want. If you are trying to get rides to frequent events, like practice, meetings, or rehearsal, suggest setting up a carpool. Have your parents come together with a few other friends' parents. Decide on a carpool schedule that benefits everyone. That way, you get rides to all the things you need, your parents give you a ride, but the responsibility is spread among multiple people. One of the best bargaining strategies is compromise. Maybe your parents can't take you to the movies this week, but they can next week. It's not exactly what you want, but it's not a no. Your parents are still willing to give you a ride. Accept that gratefully. Another compromise might be deciding on which ride to take. If you need to go to practice, the store, your friend's house, and the movies, your parents might not have time to take you to all those places. If your parents offer to take you to practice and one other thing, then compromise with them.
Summary: Propose to do a favor in return. Do something nice before you ask. Offer to pay for gas. Suggest a carpool. Compromise.

In one sentence, describe what the following article is about: Use a natural sea sponge (sponges harvested from the sea) for an interesting, multi-layered effect, similar to the look of granite (but with any color you choose). You can find natural sponges for around $10 (£7.10) at a hardware store.  Natural sea sponges often come in sizes of 5–6 in (13–15 cm). You can use a kitchen sponge, but it won't look quite the same. Choose the colors that you want to paint with and pour them into separate disposable bowls. You can use foam bowls, paper bowls, or regular bowls that you've set aside for craft use (just remember they'll be dirty afterwards). Run water over the sponge enough to get it damp, then crush it with your hands until the water no longer runs out. If you don't wring the sponge out, your paint may come out too watery and not adhere to the foam well. Choosing the paint you want to use, dip the sponge into it, blotting a little bit of paint off the sponge onto the newspaper so that you don’t make drips on your foam. Try practicing your sponge painting on the newspaper before moving to the foam; this will give you a better idea of what you want to do on your project. Touch the sponge to the foam gently, letting it rest on the foam for a few seconds before pulling it away. Repeat until the entire project is covered in paint.  Try rotating the sponge while painting to get different effects. Dampen the sponge with clean water and wring it out before choosing another color. It's important to let the paint dry before adding another coat, or it may end up looking uneven. You can wait up to 60 minutes to ensure the paint dries fully. Use the same technique to paint another coat. Focus on spots where the paint has seeped in and left white spots. Aim to create an even layer so that all the foam is covered. Give your foam project at least an hour to dry before picking it up. Wash your sponge in clean water and wring it out thoroughly, then let it dry in a ventilated area. Be sure to wash your hands with soap and warm water after handling paints.
Summary:
Use natural sponges for an artsy, granite-like effect. Put acrylic, water-based paints in separate disposable bowls. Dampen a sponge with water and wring it out. Dip the sponge into the paint, then blot some onto the newspaper. Paint by applying the sponge softly to the foam’s surface. Wait at least 15 minutes for the paint to dry. Apply another coat of paint. Let your project dry for an hour and wash your sponge.