Learn how to use the Algebra Calculator to solve systems of equations. Show
Example ProblemSolve the following system of equations: How to Solve the System of Equations in Algebra CalculatorFirst go to the Algebra Calculator main page. Type the following:
Try it now: x+y=7, x+2y=11 Clickable DemoTry entering x+y=7, x+2y=11 into the text box. After you enter the system of equations, Algebra Calculator will solve the system x+y=7, x+2y=11 to get x=3 and y=4. More ExamplesHere are more examples of how to solve systems of equations in Algebra Calculator. Feel free to try them now.
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Some word problems require the use of systems of linear equations . Here are clues to know when a word problem requires you to write a system of linear equations:
Such problems often require you to write two different linear equations in two variables. Typically, one equation will relate the number of quantities (people or boxes) and the other equation will relate the values (price of tickets or number of items in the boxes). Here are some steps to follow: 1. Understand the problem.
2. Translate the problem to an equation.
3. Carry out the plan and solve the problem.
Example: The cost of admission to a popular music concert was $ 162 for 12 children and 3 adults. The admission was $ 122 for 8 children and 3 adults in another music concert. How much was the admission for each child and adult? 1 . Understand the problem:
2 . Translate the problem to an equation.
3 . Carry out the plan and solve the problem.
If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Solving Systems of EquationsReal World ProblemsWow! You have learned many different strategies for solving systems of equations! First we started with Graphing Systems of Equations. Then we moved onto solving systems using the Substitution Method. In our last lesson we used the Linear Combinations or Addition Method to solve systems of equations. Now we are ready to apply these strategies to solve real world problems! Are you ready? First let's look at some guidelines for solving real world problems and then we'll look at a few examples. Steps For Solving Real World Problems
Ok... let's look at a few examples. Follow along with me. (Having a calculator will make it easier for you to follow along.) Example 1: Systems Word ProblemsYou are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs
and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold? Solution1. Let's start by identifying the important information:
2. Define your variables.
In this problem, I don't know how many hot dogs or sodas were sold. So this is what each variable will stand for. (Usually the question at the end will give you this information). Let x = the number of hot dogs sold Let y = the number of sodas sold 3. Write two equations. One equation will be related to the price and one equation will be related to the quantity (or number) of hot dogs and sodas sold. 1.50x + 0.50y = 78.50 (Equation related to cost) x + y = 87 (Equation related to the number sold) 4. Solve! We can choose any method that we like to solve the system of equations. I am going to choose the substitution method since I can easily solve the 2nd
equation for y. 5. Think about what this solution means. x is the number of hot dogs and x = 35. That means that 35 hot dogs were sold. y is the number of sodas and y = 52. That means that 52 sodas were sold. 6. Write your answer in a complete sentence. 35 hot dogs were sold and 52 sodas were sold. 7. Check your work by substituting. 1.50x + 0.50y = 78.50 1.50(35) + 0.50(52) = 78.50 52.50 + 26 = 78.50 AND x + y = 87 35 + 52 = 87 Since both equations check properly, we know that our answers are correct!
Example 2: Another Word ProblemYou and a friend go to Tacos Galore for lunch. You order three soft tacos and three
burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost? 1. Let's start by identifying the important information:
2. Define your variables.
In this problem, I don't know the price of the soft tacos or the price of the burritos. Let x = the price of 1 soft taco Let y = the price of 1 burrito 3. Write two equations. One equation will be related your lunch and one equation will be related to your friend's lunch. 3x + 3y = 11.25 (Equation representing your lunch) 4x + 2y = 10 (Equation representing your friend's lunch) 4. Solve! We can choose any method that we like to solve the system of equations. I am going to choose the combinations method. 5. Think about what the solution means in context of the problem. x = the price of 1 soft taco and x = 1.25. That means that 1 soft tacos costs $1.25. y = the price of 1 burrito and y = 2.5. That means that 1 burrito costs $2.50. Yes, I know that word problems can be intimidating, but this is the whole reason why we are learning these skills. You must be able to apply your knowledge! If you have difficulty with real world problems, you can find more examples and practice problems in the Algebra Class E-course. Take a look at the questions that other students have submitted:
Need More Help With Your Algebra Studies? Get access to hundreds of video examples and practice problems with your subscription! Click here for more information on our affordable subscription options. Not ready to subscribe? Register for our FREE Pre-Algebra Refresher course. How do you solve system of equations word problems?Writing Systems of Linear Equations from Word Problems. Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find. ... . Translate the problem to an equation. Assign a variable (or variables) to represent the unknown. ... . Carry out the plan and solve the problem.. What are the 7 steps in solving worded problem?A proven step-by-step method for solving word problems is actually quite simple.. Read the problem out loud to yourself.. Draw a Picture.. Think “What do I need to find?”. List what is given.. Find the key words.. Solve.. Check your work.. What are the 4 steps in order to solve word problems?Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:. Step 1: Understand the problem.. Step 2: Devise a plan (translate).. Step 3: Carry out the plan (solve).. Step 4: Look back (check and interpret).. What are the methods to solve a system of equations?There are three methods used to solve systems of equations: graphing, substitution, and elimination.
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