Formal Geometry Algebra Review

Transcription

1 Formal Geometry Algebra Review Day Solve Linear Equations and Inequalities Objectives: SWBAT solve linear equations and inequalities. SWBAT use a formula. SWBAT isolate any variable in a formula or literal equation. Equations A statement of two mathematical Epressions that are equal Inequalities A statement of two mathematical Epressions that are not equal GOLDEN RULE OF SOLVING LINEAR EQUATIONS What you do to one side you must do to the other to preserve equality. Si Steps to help solve equations.. Distributive Property a. 4( ) 4( ) 4() 8. Combine like terms that are on the same side of the = sign a. Combine constants and like variables b. Assume that you are adding them all together and sometimes you re adding a positive and negative number c.. If there are variables on each side of the = sign, find the smallest variable and move it to the other side. a. Sometimes the it is the smallest number others it can be the most negative number b. If the two coefficients are the same, add/subtract from both sides and see if the answer makes sense of not i. 6 No Solution ii. All Real Numbers / Infinate Solutions c. y 4 4y 4. Solve the two step equation by isolating the variable term a. The variable term can be,,, or 4 b. Subtract or add the constants so that you get a variable term = a number

2 5. Multiply/Divide the coefficient of the variable so that there is a single positive variable = a number a. 4 or y b. If you have a fraction attached to your variable, multiple both sides by the reciprocal of that fraction. 6. Check your work a. Put back into the equation, and see if you get the same answer on both sides of the = sign Solve the following equations w. 5 m 6 w w w 5 0 w w 0 4. n 6 n or 5 m 6 5 m m 6 m m m n 6 n4 n n 6 n n or

3 () Infinately Many Solutions Formulas and Rewriting Equations ( 6) False Statement NO SOLUTION You apply the same rules for solving, but you don t combine unlike terms. Eamples Solve each equation for the indicated variable A b b h, for b 0. a + b = c, for a. a b c b b a c b a c b a c b A bb h A b b h A b b h A b b h h h A bb h b b A b b h

4 Day Solving Systems of Equations by Substitution Objectives: SWBAT solve systems of equations by graphing. SWBAT solve systems of equations by Substitution System of Linear Equations Two or more equations with the same variable make-up Solution to a system of Linear Equations A Point Introduction to Substitution Take the value of one variable and plug it into the second equation. Find the solution to the system. 6 y. 6 y 8 y is already solved for, so plug it into the other equation. y is already solved for, so plug it into the other equation. y y 6 y y 9 6y ,9 0, 8 0 0

5 Solving Systems of Equations by Substitution ) Look at the system of equations. Decide which problem will be the easiest to isolate a variable. You have 4 ways to proceed WORKER SMARTER NOT HARDER ) Decide which variable you want to solve for, and isolate that variable. ) Plug or Substitute the equation into the variable into the other equation, solve for the single variable. 4) Substitute the value of the first variable, and plug it back into the first equation. Solve for the Second equation. This will produce the part of your answer. 5) Check it! Put both values into both equations to see if it checks out. 6) ***** If the two equations are the same, the answer is infinite solutions. ****** If the two equations are parallel, then there is no solution. ***** If your Math is good, it does not matter where you start substituting! The answer will be the same******* Solve the following systems of equations using substitution.. y = + and y + = 4. y + = 5 and y = y v y y y y y Answer, y y 5 y y 5 v y y 9 5 4y 9 5 4y 4 y y Answer, y 5 5 y

6 5. 4 y = and + y = y = 0 and y 6 = 4 y Answer, y 4 4 y4 y4 y 4 y 4 y 4 y y y0 44 y 4 y 4 y y y 4 y y Answer 4, 7. y = + 0 and y = 5 v y y 5 y 5 5 y 5 5 y Answer 5 5,

7 8. On a construction job there are 8 individuals working at a site. The foremen on the site earn $0 per day and the laborers earn $60 a day. How many laborers and how many foremen are on the site if the daily payroll is $50? Define your Variables Write your Equations Solve foreman y laborers y8 060 y50 y8 y8 060y y8 y 8 4 y 4 Answer 4 foreman 4 laborers

8 Day Factoring and Solving Trinomials when a = Objectives: SWBAT factor easy trinomials, trinomials with a leading coefficient of. SWBAT solve a quadratic equation with a leading coefficient of. SWBAT factor quadratics using substitution. The X Factoring Method when a= b c PUT IN STANDARD FROM Put c in top, b on bottom Find the factors that multiply to c and add to b 4 Set up parenthesis with those to factors factor factor Factor trinomials in the form + b + c (using the -factor).. 7. n n

9 Zero Product Rule GCF a ab0 then 0 and/or b0 a number all terms can be divided by Find the roots of a + b + c = 0 (By factoring and using the zero product rule) = = 7. Find the zeros of: f() = = =

10 Solve the following equations. Algebra Review Day Homefun. =. 6 = 6. 6 = = < 6. = 8 7. y 8. 5 = =.5 y a = 4. 7 =. 4a = 7a ( ) = 6 + All Re al Numbers No Solution 6. 8 = 4(f ) f 7. 5(y + ) 6 > 5y + 4 f 0 No Solution

11 Solve the following formulas for the variable indicated. 8. y = m + b; solve for 9. y m b m z ; solve for s zs m 0. The volume of a pyramid is given by the formula V b h, where V is the volume of the pyramid, b is the length of one side of the base, and h is the height of the pyramid. Rewrite the equation so that it would give you the height of the pyramid, for a known volume and base length. h V b. You have two summer jobs. In the first job, you work 5 hours per week and earn $7.75 per hour. In the second job, you earn $6.5 per hour and can work as many hours as you want. you want to earn $50 per week. How many hours must you work at the second job? (You must write the equation(a) and solve it(b))

12 Algebra Review Day Homefun. y = 4 and + y = 5. = 4y and + y = 0. y = 4 and y = 9,4 8,, y = 8 and 4y = y = 84 and 7y = 7 6. y = and 6y = 6 5, 4,5 8, 5, y = 60 and 5 y = y + = and y + =,0 9. Two families go to a hockey game. The Keatons purchases two adult tickets and four youth tickets for $8. The Cosby family buys four adult tickets and five youth tickets for $ How much are youth tickets to the hockey game? Adult $7 Youth $ If Snoop is 6 years older than Dre and the sum of their ages is 78, how old is that rascal Snoop who has his mind on his money and his money on his mind. Snoop 4 Dre 6

13 Algebra Review Day Homefun Factor or solve the following quadratics. (Be careful!!! Only solve if there is an = sign.) 6) r 6r 5 7) s s 6 0 r, r s 4,