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PORTFOLIO PAGE -- LINEAR FUNCTIONS 2 HONORS ALGEBRA 2 GENERAL FORMS OF EQUATIONS: Slope-Intercept Form: y = mx + b; m is slope, b is y-intercept Point-Slope Form: y โ y1 = m(x โ x1) Standard Form: Ax + By = C LESSON 1.3: LINE To find the LINE a) b) c) d) e) OF BEST FIT OF BEST FIT: Determine independent (x) vs. dependent (y) variable Plot data points Estimate trend line Choose two points ON THE LINE Calculate slope and write equation of line. (start with Point-slope form) SYSTEMS OF x Y 2 3 4 4 7 6 9 8 EQUATIONS A system of two linear equations in two variables, x and y, consists of two equations of the form ๐๐ + ๐๐ = ๐ เต . ๐ ๐ + ๐๐ = ๐ A solution to the system is an ordered pair (x, y) that satisfies BOTH equations. Ex: Solve the system by graphing: แ 2๐ฅ + 4๐ฆ = 12 ๐ฅ+๐ฆ = 2 SOLVING SYSTEMS USING SUBSTITUTION --Best for systems when there is a variable term that has a coefficient of 1 ๐ฅ + 6๐ฆ = 2 แ 5๐ฅ + 4๐ฆ = 36 SUBSTITUTION METHOD: 1) Solve one equation for one of its variables. (Hint: look for a coefficient of 1) 2) Substitute this expression into the other equation. Now you have an equation with only one variable. Solve it. 3) Substitute this value in the revised first equation and solve. 4) Write an ordered pair. Check the solution in each equation. SOLVING SYSTEMS USING ELIMINATION --get opposite coefficients on same variable terms, then add equations ELIMINATION METHOD: 1) Arrange equations with like terms in columns (like terms under each other). 2) Multiply one (or both) equation(s) by a number to obtain opposite coefficients for either the x or the y terms. (LCM of the coefficients) 3) Add the equations (one variable should now be eliminated). Solve the resulting equation. 4) Substitute the result of step 3 into one of the original equations to solve for the other variable. 5) Write in ordered pair form and check the solution in each of the original equations. แ Algebraic solutions indicating a) no solution 2๐ฅ + 8๐ฆ = โ8 3๐ฅ โ 5๐ฆ = 22 b) infinitely many solutions 6๐ฅ โ 3๐ฆ = 2 2 แ โ6๐ฅ + 3๐ฆ = 3 ๐ฅ + 5๐ฆ = 1 แ 2๐ฅ = 2 โ 10๐ฆ LESSON 1.4: SOLVING SYSTEMS Triangular Form: THREE VARIABLES Elimination: ๏ฌx ๏ญ y ๏ซ z ๏ฝ 4 ๏ฏ ๏ญy ๏ซ z ๏ฝ 5 ๏ฏz ๏ฝ 3 ๏ฎ APPLICATIONS IN ๏ฌ๏ญ 2 x ๏ซ y ๏ซ 3 z ๏ฝ 7 ๏ฏ ๏ญx ๏ซ 2 y ๏ซ z ๏ฝ 4 ๏ฏ2 x ๏ญ 3 y ๏ญ 2 z ๏ฝ ๏ญ10 ๏ฎ OF SYSTEMS OF EQUATIONS (2- AND 3- VARIABLE SYSTEMS) Ex1: There are 55 coins made up of dimes and nickels in a piggy bank. The total value is $4.00. Write the system to find how many coins there are of each type. Ex2: The difference of two numbers is 24. Their sum is 60. Write the system to find the two numbers. Ex3: A stadium has 49,000 seats. Seats sell for $25 in Section A, $20 in section B, and $15 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,052,000 from each sold-out event. How many seats does each section hold? Ex4: A change machine contains nickels, dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are five times as many nickels as dimes. Find the number of coins of each type in the machine. M. Murray