Quiz Date 1/22/19 Change For version B #5 𝒚=𝟐𝒙+𝟔 𝒚=𝟓𝒙 Pick up your homework from the back table Work on your quiz No EQ and No Warm-up. Change For version B #5 𝒚=𝟐𝒙+𝟔 𝒚=𝟓𝒙 Essential Question: None Yes you can used your notes Warm Up: None When done, turn in your quiz and any work to the BACK TABLE Then, work on this week’s homework.

Tuesday 01/22/19 Homework solution Solve the system of equation by any method 1. 𝑦=− 1 2 𝑥+2 𝑦=𝑥+8 Solve by graphing because the equations are in slope intercept form of 𝑦=𝑚𝑥+𝑏 𝑦=− 1 2 𝑥+2 First equation Slope = − 1 2 y-intercept is 2 𝑦=𝑥+8 Second equation Slope = 1 1 y-intercept is 8 𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏 ( −4, 4)

Tuesday 01/22/19 Homework solution Solve the system of equation by any method 2. 𝑦−2𝑥=3 2𝑦−12=𝑥 Solve by Substation because the x is already solve for Step 1: Determine the equation that is solve for 𝑥=2𝑦−12 Step 2: Substitute the solve equation into the other equation 𝑦−2 2𝑦−12 =3 Step 3: Simplify and solve for the variable 𝑦−4𝑦+24=3 Distribute −3𝑦+24=3 Combine the variable −3𝑦=−21 Subtract 24 to both sides 𝑦=7 Divide by -3 to both sides

WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 2,7) Step 4: Substitute the solved variable back into the original to get the other variable 𝑦−2𝑥=3 First equation (7)−2𝑥=3 Substitute 𝑦=7 7−2𝑥=3 −2𝑥=−4 Subtract 7 to both sides 𝑥=2 Divide by -2 to both sides The solution of a system is always in the format of an order pair (7,2) WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 2,7)

Tuesday 01/22/19 Homework solution Solve the system of equation by any method 3. 𝑦=2𝑥+3 𝑦= 1 2 𝑥+6 Solve by graphing because the equations are in slope intercept form of 𝑦=𝑚𝑥+𝑏 𝑦=2𝑥+3 First equation Slope = 2 1 y-intercept is 3 𝑦= 1 2 𝑥+6 First equation Slope = 1 2 y-intercept is 6 𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏 ( 2, 7)

5.3 Solve System by Elimination Date 1/23/19 Copy down Essential Question. Work on Warm Up. Essential Question How would you describe the process of solving for a system using Elimination? Warm Up: Explain the different between the two things. 𝑥+3𝑦=−2 𝑥=3𝑦+16 𝑥+3𝑦=−2 𝑥−3𝑦=16 Solve by substitution DON’T Solve by substitution

Understand when to solve by Elimination 𝑥+3𝑦=−2 𝑥=3𝑦+16 𝑥+3𝑦=−2 𝑥−3𝑦=16 Solve by substitution DON’T Solve by substitution 𝒙 is already solve for notice 𝑥=3𝑦+16 nothing is solve for For this we use Elimination

How to solve by Elimination 𝑥+3𝑦=−2 𝑥−3𝑦=16 Step 1: check that the coefficient of the one of the variable are opposites. 𝑥+3𝑦=−2 𝑥−3𝑦=16 The coefficient of the y are opposites Step 2: Add the two equations(one variable should disappear) . One equation with one unknown

Step 3: Solve for the variable you have left Step 4: Substitute the solved variable back into one of the original equation to solve for other variable. The solution needs to be in a order pair.

Checking your answer The solution is (7, −3) Equation 1 𝑥+3𝑦=−2 (7)+3(−3)=−2 −2=−2 Equation 2 𝑥−3𝑦=16 7 −3(−3)=16 16=16

Wednesday 01/23/19 Homework solution Solve the system of equation by elimination 1. 3𝑦+2𝑥=6 5𝑦−2𝑥=10 Solve by elimination because the coefficient of x are opposite Step 1: check that the coefficient of the one of the variable are opposites. 3𝑦+2𝑥=6 5𝑦−2𝑥=10 Step 2: Add the two equations together (one variable should disappear) 3𝑦+2𝑥=6 5𝑦−2𝑥=10 8𝑦 =16 Step 3: Simplify and solve for the variable 8𝑦=16 𝑦=2 Divide by 8 to both sides

WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 0, 2) Step 4: Substitute the solved variable back into the original to get the other variable 3𝑦+2𝑥=6 First equation 3(2)−2𝑥=6 Substitute 𝑦=2 6−2𝑥=6 −2𝑥=0 Subtract 6 to both sides 𝑥=0 Divide by -2 to both sides The solution of a system is always in the format of an order pair (2,0) WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 0, 2)

Wednesday 01/23/19 Homework solution Solve the system of equation by elimination 2. 5𝑦+4𝑥=22 −12𝑦−4𝑥=−36 Solve by elimination because the coefficient of x are opposite Step 1: check that the coefficient of the one of the variable are opposites. 5𝑦+4𝑥=22 −12𝑦−4𝑥=−36 Step 2: Add the two equations together (one variable should disappear) 5𝑦+ 4𝑥 = 22 −12𝑦−4𝑥 =−36 −7𝑦 =−14 Step 3: Simplify and solve for the variable −7𝑦=−14 𝑦=2 Divide by -7 to both sides

WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 3, 2) Step 4: Substitute the solved variable back into the original to get the other variable 5𝑦+4𝑥=22 First equation 5 2 +4𝑥=22 Substitute 𝑦=2 10+4𝑥=22 4𝑥=12 Subtract 10 to both sides 𝑥=3 Divide by 4 to both sides The solution of a system is always in the format of an order pair (2,3) WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 3, 2)

Wednesday 01/23/19 Homework solution Solve the system of equation by elimination 3. 3𝑥−𝑦=5 𝑥+𝑦=3 Solve by elimination because the coefficient of y are opposite Step 1: check that the coefficient of the one of the variable are opposites. 3𝑥−𝑦=5 𝑥+𝑦=3 Step 2: Add the two equations together (one variable should disappear) 3𝑥 − 𝑦 = 5 𝑥 + 𝑦 = 3 4𝑥 =8 Step 3: Simplify and solve for the variable 4𝑥=8 𝑥=2 Divide by 4 to both sides

Correct order pair ( 2, 1) An order pair is ( 𝑥, 𝑦) Step 4: Substitute the solved variable back into the original to get the other variable 𝑥+𝑦=3 second equation (2)+𝑦=3 Substitute x=2 2+𝑦=3 y=1 Subtract 2 to both sides The solution of a system is always in the format of an order pair Correct order pair ( 2, 1) An order pair is ( 𝑥, 𝑦)

5.3 Solve System by Elimination Day 2 Date 1/24/19 Copy down Essential Question. Work on Warm Up. Fix error on homework Essential Question How is solving a system using elimination different that solving using substitution? Warm Up: Add the two equation in each problem. 1. 2. 𝑥−2𝑦 = −19 5𝑥+2𝑦 = 1 3𝑥+4𝑦 =18 −2𝑥+4𝑦 = 8 6𝑥 =−18 𝑥+8𝑦=26

Describe the process of solving a system by Elimination in your own words 3𝑥+2𝑦=4 3𝑥−2𝑦=−4 Step 1: Step 2:

Step 3: Step 4: The solution needs to be in a order pair.

Practice on solving by Elimination 2𝑥−𝑦=9 4𝑥+𝑦=21 Step 1: check that the coefficient of the one of the variable are opposites. 2𝑥−1𝑦=9 4𝑥+1𝑦=21 The coefficient of the y are opposites Step 2: Add the two equations(one variable should disappear) .

Step 3: Solve for the variable you have left Step 4: Substitute the solved variable back into one of the original equation to solve for other variable. The solution needs to be in a order pair. The solution is (5, 1)

How to solve by Elimination when there is the same number but they are not opposite 3𝑥+4𝑦=18 −2𝑥+4𝑦=8

How to solve by Elimination when there is the same number but they are not opposite Step 1: check that the coefficient of the one of the variable are opposites. 3𝑥+4𝑦=18 −2𝑥+4𝑦=8 Step 1b: 3𝑥+4𝑦=18 −1(−2𝑥+4𝑦=8) Result 3𝑥+4𝑦=18 2𝑥−4𝑦=−8

3𝑥+ 4𝑦 = 18 2𝑥 −4𝑦 =−8 5𝑥 =10 (2, 3) Solution An order pair is ( 𝑥, 𝑦) Step 2: Add the two equations together (one variable should disappear) 3𝑥+ 4𝑦 = 18 2𝑥 −4𝑦 =−8 5𝑥 =10 Step 3: Simplify and solve for the variable 5𝑥=10 𝑥=2 Divide by 5 to both sides Step 4: Substitute the solved variable back into the original to get the other variable 3𝑥+4𝑦=18 First equation 3(2)+4𝑦=18 Substitute x=2 6+4𝑦=18 4𝑦=12 Subtract 6 to both sides 𝑦=3 Divide by 4 to both sides The solution of a system is always in the format of an order pair (2, 3) Solution An order pair is ( 𝑥, 𝑦)

Practice on solving a system by Elimination 3𝑥+3𝑦=15 −2𝑥+3𝑦=−5

Practice on solving a system by Elimination Step 1: check that the coefficient of the one of the variable are opposites. 3𝑥+3𝑦=15 −2𝑥+3𝑦=−5 Step 1b: 3𝑥+3𝑦=15 −1(−2𝑥+3𝑦=−5) Result 3𝑥+3𝑦=15 2𝑥−3𝑦=5

3𝑥+3𝑦 = 15 2𝑥−3𝑦 = 5 5𝑥 =20 (4, 1) Solution An order pair is ( 𝑥, 𝑦) Step 2: Add the two equations together (one variable should disappear) 3𝑥+3𝑦 = 15 2𝑥−3𝑦 = 5 5𝑥 =20 Step 3: Simplify and solve for the variable 5𝑥=20 𝑥=4 Divide by 5 to both sides Step 4: Substitute the solved variable back into the original to get the other variable 3𝑥+3𝑦=15 First equation 3(4)+3𝑦=15 Substitute x=4 12+3𝑦=15 3𝑦=3 Subtract 12 to both sides 𝑦=1 Divide by 4 to both sides The solution of a system is always in the format of an order pair (4, 1) Solution An order pair is ( 𝑥, 𝑦)

Thursday 01/24/19 Homework solution Solve the system of equation by elimination 1. 7𝑥+4𝑦=2 9𝑥−4𝑦=30 Solve by elimination because the coefficient of y are opposite Step 1: check that the coefficient of the one of the variable are opposites. 7𝑥+4𝑦=2 9𝑥−4𝑦=30 Step 2: Add the two equations together (one variable should disappear) 7𝑥+ 4𝑦 = 2 9𝑥 −4𝑦 = 30 16𝑥 =32 Step 3: Simplify and solve for the variable 16𝑥=32 𝑥=2 Divide by 16 to both sides

Correct order pair (2, −3) An order pair is ( 𝑥, 𝑦) Step 4: Substitute the solved variable back into the original to get the other variable 7𝑥+4𝑦=2 First equation 7(2)+4𝑦=2 Substitute x=2 14+4𝑦=2 4𝑦=−12 Subtract 14 to both sides 𝑦=−3 Divide by 4 to both sides The solution of a system is always in the format of an order pair Correct order pair (2, −3) An order pair is ( 𝑥, 𝑦)

Thursday 01/24/19 Homework solution Solve the system of equation by elimination 2. 3𝑥−4𝑦=−5 5𝑥−2𝑦=−6 Solve by elimination because the coefficient of y are opposite Step 1: check that the coefficient of one of the variables are opposites. They are not, so we need to make one of them something else 3𝑥−4𝑦=−5 −𝟐∙(5𝑥−2𝑦=−6) Multiple the second equation by -2 Step 1 again: check that the coefficient of the one of the variables are opposites. 3𝑥−4𝑦=−5 −10𝑥+4𝑦=12) We are good now Step 2: Add the two equations together (one variable should disappear) 3𝑥 + −4𝑦 = −5 −10𝑥 +4𝑦 =12 −7𝑥 =7 Step 3: Simplify and solve for the variable −7𝑥=7 𝑥=−1 Divide by -7 to both sides

Correct order pair (−1, 1 2 ) An order pair is ( 𝑥, 𝑦) Step 4: Substitute the solved variable back into the original to get the other variable 3𝑥−4𝑦=−5 First equation 3(−1)−4𝑦=−5 Substitute x=−1 −3−4𝑦=−5 −4𝑦=−2 Add 3 to both sides 𝑦= 2 4 𝑜𝑟 1 2 Divide by -4 to both sides The solution of a system is always in the format of an order pair Correct order pair (−1, 1 2 ) An order pair is ( 𝑥, 𝑦)

Thursday 01/24/19 Homework solution Solve the system of equation by elimination 3. 2𝑥+3𝑦=8 3𝑥+2𝑦=7 Solve by elimination because the coefficient of y are opposite Step 1: check that the coefficient of one of the variables are opposites. They are not, so we need to make both of them something else 𝟑∙ 2𝑥+3𝑦=8 Multiple the first equation by 3 −𝟐∙ 3𝑥+2𝑦=7 Multiple the second equation by −2 Step 1 again: check that the coefficient of the one of the variables are opposites. 6𝑥+9𝑦=24 −6𝑥−4𝑦=−14 We are good now Step 2: Add the two equations together (one variable should disappear) 6𝑥+9𝑦=24 −6𝑥−4𝑦=−14 5𝑦 =10 Step 3: Simplify and solve for the variable 5𝑦=10 𝑦=2 Divide by 5 to both sides

Correct order pair (1, 2) An order pair is ( 𝑥, 𝑦) Step 4: Substitute the solved variable back into the original to get the other variable 2𝑥+3𝑦=8 First equation 2𝑥+3(2)=8 Substitute y=2 2𝑥+6=8 2𝑥=2 Subtract 6 to both sides 𝑥=1 Divide by 2 to both sides The solution of a system is always in the format of an order pair Correct order pair (1, 2) An order pair is ( 𝑥, 𝑦)

5.3 Solve System by Elimination Day 3 Date 1/25/19 Turn in your homework to the back table. Copy down Essential Question. Work on Warm Up. Essential Question Why do the coefficient in a system of equation need to be opposite values of each other? Warm Up: Add the two equation in each problem. 1. −𝑥 +𝑦=5 𝑥−5𝑦=−9 2. 𝑥−10𝑦=60 𝑥+14𝑦=12 3. 2𝑥+3𝑦=12 5𝑥−𝑦=13 −4𝑦=−4 2𝑥+4𝑦=72 7𝑥+2𝑦=25

Exploration activity: Solving by Elimination 2. 1𝑥−10𝑦=60 1𝑥+14𝑦=12 2x + 4y = 72 2. 𝑥−10𝑦=60 𝑥+14𝑦=12 2x + 4y = 72 3. 2𝑥+3𝑦=12 5𝑥−1𝑦=13 7x + 2y = 25 3. 2𝑥+3𝑦=12 5𝑥−1𝑦=13 7x + 2y = 25 Step 1: check that the coefficient of the one of the variable are opposites. Step 1: check that the coefficient of the one of the variable are opposites. Step 1b: multiple by a -1 to get the opposite value. Step 1b: multiple by a -1 to get the opposite value. 2𝑥+3𝑦=12 −1∙(5𝑥−1𝑦=13) 1𝑥−10𝑦=60 −1∙(1𝑥+14𝑦=12) 2𝑥+3𝑦=12 −5𝑥+1𝑦=−13 2𝑥+3𝑦=12 −5𝑥+1𝑦=−13 1𝑥−10𝑦=60 −1𝑥−14𝑦=−12 1𝑥−10𝑦=60 −1𝑥−14𝑦=−12 Step 1: check that the coefficient of the one of the variable are opposites. Step 1: check that the coefficient of the one of the variable are opposites.

How to Solve by Elimination by multiplying first 2𝑥+3𝑦=12 5𝑥−1𝑦=13 Step 1: check that the coefficient of the one of the variable are opposites. 2𝑥+3𝑦=12 5𝑥−1𝑦=13 Step 1b: multiple by (something) to get the opposite value. 2𝑥+3𝑦=12 3∙(5𝑥−𝑦=13) Multiple by 3 to the second equation 2𝑥+3𝑦=12 15𝑥−3𝑦=39 Step 1: check that the coefficient of the one of the variable are opposites. 2𝑥+3𝑦=12 15𝑥−3𝑦=39

2𝑥 + 3𝑦 = 12 15𝑥 − 3𝑦 = 39 17𝑥 = 51 (3, 2) Solution Step 2: Add the two equations together (one variable should disappear) 2𝑥 + 3𝑦 = 12 15𝑥 − 3𝑦 = 39 17𝑥 = 51 Step 3: Simplify and solve for the variable 17𝑥=51 𝑥=3 Divide by 17 to both sides Step 4: Substitute the solved variable back into the original to get the other variable 2𝑥+3𝑦=12 First equation 2(3)+3𝑦=12 Substitute x=3 6+3𝑦=12 3𝑦=6 Subtract 6 to both sides 𝑦=2 Divide by 3 to both sides The solution of a system is always in the format of an order pair (3, 2) Solution An order pair is ( 𝑥, 𝑦)

or Practice on solving by Elimination by multiplying first 2𝑥+𝑦=3 𝑥−3𝑦=12 Step 1: check that the coefficient of the one of the variable are opposites. 2𝑥+𝑦=3 1𝑥−3𝑦=12 or 2𝑥+1𝑦=3 1𝑥−3𝑦=12 Step 1b: multiple by (something) to get the opposite value. 2𝑥+𝑦=3 −2∙(1𝑥−3𝑦=12) Multiple by -2 to the second equation 2𝑥+𝑦=3 −2𝑥+6𝑦=−24 Step 1: check that the coefficient of the one of the variable are opposites. 2𝑥+𝑦=3 −2𝑥+6𝑦=−24

2𝑥 + 𝑦 =3 −2𝑥 + 6𝑦 =−24 7𝑦=−21 (3, −3) Solution Step 2: Add the two equations together (one variable should disappear) 2𝑥 + 𝑦 =3 −2𝑥 + 6𝑦 =−24 7𝑦=−21 Step 3: Simplify and solve for the variable 7𝑦=−21 𝑦=−3 Divide by 7 to both sides Step 4: Substitute the solved variable back into the original to get the other variable 2𝑥+𝑦=3 First equation 2𝑥+ −3 =3 Substitute y=−3 2x−3 =3 2𝑥=6 Add 3 to both sides 𝑥=3 Divide by 2 to both sides The solution of a system is always in the format of an order pair (3, −3) Solution An order pair is ( 𝑥, 𝑦)

Math Talk Which is incorrect? Explain the error