Replace x in the first equation with the given value of x in the second equation. Having isolated x in the second equation, we can then replace the x in the first equation with the equivalent value from the second equation: (18 - 3y).ġ. If that were not the case, we would first need to simplify the equation to isolate x. In the second equation, x is already isolated. With this method, you are essentially simplifying one equation and incorporating it into the other, which allows you to eliminate one of the unknown variables.Ĭonsider the following system of linear equations:
I am going to choose the combinations method.Another way to solve a system of equations is by substitution. 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? This step-by-step online calculator will help you understand how to solve systems of linear equations using Gauss-Jordan.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. Enter the Submit button for the calculator to process the three input equations. Enter the three equations in the blocks titled Eqn 1, Eqn 2, and Eqn 3, respectively. Each hot dog costs $1.50 and each soda costs $0.50. How To Use the 3 Systems of Equations Calculator Step 1. 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!