![]() Now we can plug in for x in either original equation. On the right side, we add 183 and (-480), this gives us (-297): $$-27x=-297$$ We can solve this equation for x by dividing each side by -27: Now we can add the left sides and set this equal to the sum of the right sides: $$\hspace$$ On the left side, we add 9x + (-36x), this gives us -27x. The y variable will be eliminated when we add our equations together. This will give us 12y in equation 1 and (-12y) in equation 2. The second equation is formed using the same thought process. The result is 183 (total revenue for day 1). ![]() We add this to the product of 12 (number of child tickets sold) and y (the cost per child ticket). In our first equation, we are multiplying 9 (number of adult tickets sold) by x ( the cost per adult ticket). We have the information for day 1 and day 2 organized in our table above. ![]() Step 3) Write two equations using both variables Step 2) Assign a variable for each unknown Step 1) What is our main objective for this problem? We want to find the cost of one adult ticket along with the cost of one child ticket. In some cases, it may help to organize the information into a table: Category What is the price each of one adult ticket and one child ticket? The school took in $160 on the second day by selling 12 adult tickets and 4 child tickets. On the first day of ticket sales, the school sold 9 adult tickets and 12 child tickets for a total of $183. Molly's school is selling tickets to a dance performance. Check the result by reading back through the problem.State the answer using a nice clear sentence.Write two equations using both variables.Assign a variable to represent each unknown.Read the problem, get a clear understanding of the objective.Six-step method for Applications of Linear Systems Let's modify our six-step process to work for applications of linear systems. We can build on that process and move into a more challenging topic that involves solving word problems that require setting up and solving a system of linear equations. We previously learned a six-step process used to set up and solve a word problem that involves a linear equation in one variable.
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