8.1/8.2 Systems of Equations… Systems of equations are sets of two or more equations that share two or more Variables… There are essentially three.

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8.1/8.2 Systems of Equations… Systems of equations are sets of two or more equations that share two or more Variables… There are essentially three ways to solve them… SUBSTITUTION GRAPHING ELIMINATION

#1SUBSTITUTION Two equations means we will be solving for two variables – the solution will be in (x, y) form. FIRST: Solve one of the equations for one variable…

ORIGINAL SYSTEM NEXT: Substitute the equation You solved for the variable in the other equation.

FINALLY: Substitute the value for the variable you solved in one of the equations and solve for the remaining variable.

Your solution is… Written as an ordered pair…

#2 GRAPHICALLY let’s look at that same system graphically… FIRST: Solve for a single variable (y if you have it) in both equations

NOW, Graph them and find the intersection – that is your solution!

#3 WORD PROBLEMS… #74 pg. 629 You are offered two jobs selling college textbooks. One company offers an annual salary of $25,000 plus a year end bonus of 1% of all your sales. The other company offers an annual salary of $20,000 plus a year end bonus of your sales. How much would you have to sell in a year to make the second offer the better offer? The first two steps in any word problem is to (1) Define your variables, and (2) Establish the relationships.

#4 ELIMINATION In this method, we add equations together to eliminate a variable. FIRST: Get two coefficients of the same variable to be numeric opposites by multiplying each equation by an appropriate constant.

NEXT: Add the equations together and solve for one variable. NOW, back substitute to solve for the other.

LOOK AT EXAMPLES 3, 4, & 5 IN YOUR TEXT!

A 10 meter by 20 meter rectangular swimming pool (the inner rectangle below) is to be surrounded by a wooden deck and a fence. The rectangle formed by the fence is to be 10 meters longer than it is wide, as shown below. If the area of the deck (the region between the inner rectangle and outer rectangle) is to be 400 square meters, what will be the dimensions of the rectangle formed by the fence (the outer rectangle)?

An investor is going to invest an amount of money, X, in a low-risk fund paying 4.5% simple interest each year, and another amount, Y, in a high-risk fund paying 8% simple interest each year. Her goal is to have the total amount of interest for the year to be $6800. In order to manage the risk involved, she requires that the amount in the fund paying 4.5% simple interest be twice as much as the amount in the fund paying 8% simple interest. Use the simple interest formula (I = prt) and find the amount that she should invest in each account. to answer the questions below.