, xn such that each of the equations is satisfied. We can choose any method that we like to solve the system of equations. A solution of a linear system is an assignment of values to the variables x1, x2. One equation will be related your lunch and one equation will be related to your friend's lunch.ģx + 3y = 11.25 (Equation representing your lunch)Ĥx + 2y = 10 (Equation representing your friend's lunch) In this problem, I don't know the price of the soft tacos or the price of the burritos. How much do soft tacos cost? How much do burritos cost? Your friend's bill is $10.00 for four soft tacos and two burritos. You order three soft tacos and three burritos and your total bill is $11.25. You and a friend go to Tacos Galore for lunch. ThinkĬarefully about what's happening in the problem when trying to write the That wasn't too bad, was it? The hardest part is writing the equations.įrom there you already know the strategies for solving. Since both equations check properly, we know that our answers are correct! Write your answer in a complete sentence.ģ5 hot dogs were sold and 52 sodas were sold. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations. In this example, the ordered pair ((4,7)) is the solution to the system of linear equations. I am going to choose the substitution method since I can easily solve the 2nd equation for y. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. We can choose any method that we like to solve the system of equations. X + y = 87 (Equation related to the number sold) 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.ġ.50x + 0.50y = 78.50 (Equation related to cost) (Usually the question at the end will give you this information). So this is what each variable will stand for. In this problem, I don't know how many hot dogs or sodas were sold. Ask yourself, "What am I trying to solve for? What don't I know?.Let's start by identifying the important information: How many hot dogs were sold and how many sodas were sold?ġ. You must report the number of hot dogs sold and the number of sodas sold. You sold a total of 87 hot dogs and sodas combined. At the end of the night you made a total of $78.50. Each hot dog costs $1.50 and each soda costs $0.50. You are running a concession stand at a basketball game. (Having a calculator will make it easier for you to follow along.) Always write your answer in complete sentences! Answer the questions in the real world problems.Check your answers by substituting your ordered pair into the original equations.
Use one of the methods for solving systems of equations to solve.Highlight the important information in the problem that will help write two equations.
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