finding solutions for 3 equation systems

The easiest equation to work with is the last one. For example, suppose the three equations are To solve a system of three linear equations in three variables by substitution, you must first identify the easiest equation to work with. Simply input the coefficients and constant terms, and the calculator will output the unique solution set if one exists. You can also use the system of equations calculator on the left. Both methods can be applied to systems with more than three variables. A more advanced technique is to use matrices.

The simplest way is to apply substitution to eliminate the variables one by one. I am going to choose the combinations method.In linear algebra, there are many methods for solving systems of linear equations in several variables. We can choose any method that we like to solve the system of equations. 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. I am going to choose the substitution method since I can easily solve the 2nd equation for y. 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.

Finding solutions for 3 equation systems