6-4: Applications of Linear Systems Algebra 1

Solving a System Graphing: When you want a __________ display of when you want to estimate the solution. Substitution: When one equation is already solved for ______of the ____________when it is easy to solve for one of the variables. Elimination: When one of the coefficients of one variable are the _________ or ____________ VISUAL ONE VARIABLES SAMEOPPOSITES

Finding a Break-Even Point Break-Even Point: The break-even point for a business is the point at which income ___________ expenses. Graphing the expenses of a company versus the income the break-even point is represented by the ______________ of the two graphs. Note that the y-value represents dollars received as _________ as well as dollars spent on ____________ EQUALS INTERSECTION INCOME EXPENSES

Finding a Break-Even Point What is the relationship of income to expenses before the break-even point is reached? What is the relationship after the break-even point is reached? The amount of income is less than the amount of the expenses. The amount of income is greater than the amount of the expenses.

Finding a Break-Even Point A carpenter makes and sells rocking chairs. The material for each chair costs $ The chairs sell for $75 each. If the carpenter spends $420 on advertising, how many chairs must she sell to break even? Let x = the number of chairs (both functions) Let y = the amount spent (expense function) Let y = the amount earned (income function) Expense:Income: We want to know when the income equals the expenses or the break even point. The carpenter must sell 8 chairs to break even.

Solving a Mixture Problem A scientist has a container of 2% acid solution and a container of 5% acid solution. How many fluid ounces of each concentration should be combined to make 25 fluid ounces of 3.2% acid solution?

Solving a Mixture Problem A scientist has a container of 2% acid solution and a container of 5% acid solution. How many fluid ounces of each concentration should be combined to make 25 fluid ounces of 3.2% acid solution? Let x = the amount of 2% solutionLet y = the amount of 5% solution Total Solution: Percent of acid in solution: The scientist should mix 15 oz. of the 2% acid solution and 10 oz. of the 5% acid solution

Homework: p #5-11, 13-17