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W ARM U P O CT. 1 ST Come in, get a tracking sheet from the basket, and quietly begin the warm up. 1. Write the ordered pair that describes a point 4 units down from and 3 units to the right of the origin. 2. Write the ordered pair that is 8 units to the left of the origin and lies on the x-axis. For #3-6, identify the quadrant for each ordered pair. 3. ( -1, 7 )4. ( 9, 2 ) 5. ( 0.75, -4 )6. ( 0, 5 ) 7. Which property makes the following true? 3(x – 5) = 3x – 15

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H OMEWORK A NSWERS – 4.1

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H OMEWORK A NSWERS ( CONT.) – 4.1

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H OMEWORK A NSWERS – 4.3

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H OMEWORK A NSWERS ( CONT.) – 4.3

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E QUATIONS A S R ELATIONS The equation y = 3x + 4 is an example of an equation in two variables because it contains x and y. A solution of an equation in 2 variables is an ordered pair. Only a certain set of ordered pairs work for this equation and make it true. What does it mean if an equation is true? It means that both sides have the same number! A REPLACEMENT SET is a set of ordered pairs that could replace x and y. We have to pick the ones that work! A SOLUTION SET is a set of ordered pairs that work for the relation.

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S OLVE U SING A R EPLACEMENT S ET 1. Find the solution set for -3 = 2x – y, given the replacement set {(-2, -1), (-1, 3), (0, 4), (3, 9)}. Make a table. Substitute the x and y-values of each ordered pair into the equation. Solution Set XY-3 = 2x – yTrue or False?

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H OW ABOUT THIS ONE ? 2. Find the solution set, given the replacement set 3x + 2y = 6{(2, 3), (0, 1), (0, 3), (2, 0)} Solution Set: XY3x + 2y = 6True or False?

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C AN YOU GET THIS ONE ON YOUR OWN ? 3. Solve 2x – 3y = 5 given the replacement set {(0, 0), (1, -1), (4, 1), (-2, 3)}

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R EMEMBER D OMAIN AND R ANGE FROM F RIDAY ? Domain = x Range = y Sometimes, we are given a domain for an equation and we need to find out the range. Note: Domain is also known as INPUT, and Range is also known as OUTPUT.

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W HEN WE ARE GIVEN D OMAIN AND A SKED TO F IND R ANGE : Step 1: Solve the equation for y if necessary. (We want to know our y-values so we need to get it by itself!) Step 2: Create a table and fill it in! Step 3: Write your ordered pairs as a solution set.

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S OLVE U SING A G IVEN D OMAIN Example: Solve 1 = 2 x – y if the domain is {-2, -1, 0, 2, 4}. Solution Set: xy(x, y)

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H OW ABOUT THIS ONE ? Find the solution set, given the domain. 4x + 8 = 2yx = {-4, -2, 0, 2, 4}. Solution Set: {(-4, ), (-2, ), (0, ), (2, ), (4, )}

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Y OU T RY ! 3. Solve y – 2 = x given the domain {-2, -1, 0, 1, 2}.

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B UT WAIT …O N F RIDAY, WE SAID THAT THERE WERE 4 WAYS TO SHOW A RELATION What were they again? Ordered pairs Table Graph Mapping Graphs are the easiest way to visually represent a relation, so lets practice graphing our solution sets.

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S OLVE AND G RAPH THE S OLUTION 1. Solve 4x + 2y = 12 if the domain is (-1, 0, 2, 4}. Graph the solution set.

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H OW ABOUT THIS ONE ? Solve y – 3x = -2 given the domain {-2, -1, 0, 1, 2}. Graph the solution set.

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Y OU T RY ! 1. Solve 2y = x + 2 given the domain {-4, -2, 0, 2, 4}. Graph the solution set.

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N OW THAT WE KNOW WHAT WE RE DOING, LET S LEARN ANOTHER WAY TO FIND SOLUTIONS TO SOME OF THESE EQUATIONS … USING OUR CALCULATOR!

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W ITH O UR C ALCULATOR ! Find the solution set, given the replacement set 4x + 2y = 8{(2, 3), (0, 1), (0, 3), (2, 0)} Solve for y. Calculator Steps: 1. 2. 3. 4. Solution Set:

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W ITH O UR C ALCULATOR ! 2. Find the solution set, given the domain. 6x + 2 = 2yx = {-4, -2, 0, 2, 4}. Solve for y. Calculator Steps: 1. 2. 3. 4. Solution Set: {(-4, ), (-2, ), (0, ), (2, ), (4, )}

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W ITH O UR C ALCULATOR ! Solve y – 4x = -5 given the domain {-2, -1, 0, 1, 2}. Graph the solution set. Solve for y. Calculator Steps: 1. 2. 3. 4. 5.

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H OMEWORK Colossal Creature Worksheet

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E XIT Q UIZ Complete on a half sheet of notebook paper. Be sure to PUT YOUR NAME AT THE TOP SO I CAN GIVE YOU CREDIT! 1. Write the solution set to the equation y = 2x + 3 if the domain is {-2, 0, 3} 2. Which of the following ordered pairs satisfy the equation y = 5 – 6x? Write them as a solution set. {(1, -1), (4, -3), (-1, 11), (-3, 23), (0, 15)} 3. Solve and graph the solution set to the following equation 6x – 3y = 9 given the domain { -2, -1, 0, 1, 2}

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V OCABULARY SHEET Throughout the year, we are learning many important math vocabulary words. Its almost like learning a new language. These words are important for your: Tests Midterm Final End of Course Test ENTIRE MATH CAREER! So, to make sure we know them, I am giving you a handy-dandy vocabulary sheet to keep in the front of your binder at all times. Each unit, we will add new words to it.

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L ET S GO BACK AND ADD SOME OLD WORDS Brainstorm: What should we add?

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Chapter 3 Lesson 2 Solving Systems of Equations Algebraically.

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