Algebra 2 & GraphingShelby Ferreira

Group ActivityThe United States population in 2005 was twice the population in 1949. If the population of the United States in 2005 was 296 million, what was the population in 1949(in millions)? Create an equation that represents this problem. Then, create a visual representation of the problem.

Solving Equations with One Variable Keep both sides of the equation balancedIsolate the variable=Keep it on one side of the equation, by itselfPerform the opposite operation of the piece of the equation you want to get rid ofTo check the solution is correct, replace it back in the original equation.Example: p+2=7

Equations with Variables on Both

Sides The process is the same as above, just more stepsExample: 5x+3=3x+7

Solving Equations with Fractions

Multiply the ENTIRE equation by the least common denominator of all the fractions in the equationThis will get rid of fractions Solve the equation as you would with whole numbersExample: x/2 + x/3 =5

Solving Equations with Decimals

Handled in a similar way to equations with fractionsMultiply both sides of the equation by a power of ten in order to get rid of any decimals and work with only whole numbersTo determine which power of ten to multiply by, determine how many decimals places are in the rightmost digit. Multiply by the inverse whole number.Example: 0.1x + 0.01x = 1.21

Inequalities Solve inequalities the same as if you were solving an equationExample: x+3 < 7HOWEVER!!! THERE IS ONE EXCEPTION! WHEN YOU MULTIPLY OR DIVIDE AN INEQUALITY BY A NEGATIVE NUMBER, REVERSE THE DIRECTION OF THE INEQUALITY SIGNExample: -2x < 14

Group ActivityKeith has $500.00 in a savings account at the beginning of the summer. He wants to have at least $200.00 in the account by the end of the summer. He withdraws $25.00 each week for food, clothes, and movie tickets.Write an inequality that represents Keith’s situation.How many weeks can Keith withdraw money from his account?Create a visual representation of the problem.

Functionsx y1 32 65 15

• Two variables• Relationship between the two variables• Can be plotted on a coordinate plane• What might these points represent?

Linear EquationWhen x and y values have a consistent relationship, the points form a lineThe line can be plotted using the equation y=mx+b

y=any y valuex=any x valuem=slop of the line (rise/run)b=y-intercept

What might such a line represent?

Systems of Linear Equations

Also called “Simultaneous equations”Two or more equations happening at the same timeThe number of equations is the number of variables to solve forThe “solution” is the point where the lines intersectEx: x+y=5 x-y=1

Elimination Method One method used to solve simultaneous equations1. Add the two equations to eliminate one of the variables. (Sometimes you must first multiply one equation by another number to get it ready for this method.)2. Substitute the solution for one variable in the original equations and solve for the other variable.Ex: x+y=5 x-y=1Ex: 5x+3y=12 -2x+3y=-3

Substitution Method Another method used to solve simultaneous equations1. Solve one equation for one variable. 2. Substitute that expression into the other equation and solve for the remaining variable.3. Substitute the solution into one of the original equations to find the second variable.Ex: y=2x 3x+3y=21

Group ActivityProblem 1:

Equation 1: 2x + y = 7 Equation 2: 3x - y = 8

Problem 2:Equation 1: 2x + y = 5Equation 2: -4x + 6y = -2

Problem 3:Equation 1: y - 2x = 1Equation 2: 2y - 3x = 5