Topic Solving Systems of Equations Using Elimination with

Topic Solving Systems of Equations Using Elimination with Addition and Subtraction.

Application In the Math Bazaar, Carmela bought 3 packs of crackers and 4 packs of peanuts and paid 27 pesos. Jane bought 3 packs of the same crackers and 6 packs of the same peanuts and paid 33 pesos. How much does each pack of crackers and peanuts cost?

Question When do we used elimination method by addition and subtraction in solving linear systems?

Recall Addition and Subtraction of Polynomials 3 x 4 y + -3 x - 4 y What can you say about adding opposite terms? What can you say about subtracting same terms?

Recall Addition and Subtraction of Polynomials 1. 3 x + 2 y = 6 + 4 x – 6 y = 10 2. -6 x + 9 y = 3 + 5 x – 11 y = 12

Polynomials 3. 5 x – 6 y = 12 + 8 x + 6 y = 15 4. 3 x + 7 y = 1 - 3 x – 2 y = 19

Polynomials 5. 5 x – 6 y = 14 - 2 x – 6 y = 3 6. 8 x + 2 y = 16 + 4 x – 2 y = 10

Solving Systems of Equations l Elimination means getting rid of something, in this case, remove a variable. Again, the idea is to have only one variable to solve for. l Elimination is easiest when the equations are in standard form.

Solving a system of equations by elimination using addition and subtraction. Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Standard Form: Ax + By = C Look for variables that have the same coefficient. Step 3: Add or subtract the equations. Solve for the variable. Step 4: Plug back in to find the other variable. Substitute the value of the variable into the equation. Step 5: Check your solution. Substitute your ordered pair into BOTH equations.

1) Solve the system using elimination. x + y = 5 3 x – y = 7 Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Add or subtract the equations. They already are! The y’s have the same coefficient. Add to eliminate y. x+ y=5 (+) 3 x – y = 7 4 x = 12 x=3

1) Solve the system using elimination. x + y = 5 3 x – y = 7 Step 4: Plug back in to find the other variable. Step 5: Check your solution. x + y = 5 (3) + y = 5 y = 2 (3, 2) (3) + (2) = 5 3(3) - (2) = 7 The solution is (3, 2). What do you think the answer would be if you solved using substitution?

2) Solve the system using elimination. 4 x + y = 7 4 x – 2 y = -2 Step 1: Put the equations in Standard Form. They already are! Step 2: Determine which variable to eliminate. The x’s have the same coefficient. Step 3: Add or subtract the equations. Subtract to eliminate x. 4 x + y = 7 (-) 4 x – 2 y = -2 3 y = 9 Remember to “keep-changey=3 change”

2) Solve the system using elimination. 4 x + y = 7 4 x – 2 y = -2 Step 4: Plug back in to find the other variable. Step 5: Check your solution. 4 x + y = 7 4 x + (3) = 7 4 x = 4 x = 1 (1, 3) 4(1) + (3) = 7 4(1) - 2(3) = -2

Which step would eliminate a variable? 3 x + y = 4 3 x + 4 y = 6 Isolate y in the first equation 2. Add the equations 3. Subtract the equations 4. Multiply the first equation by -4 1.

Which step would eliminate a variable? 8 x - y = 16 3 x +y = 6 Isolate y in the first equation 2. Add the equations 3. Subtract the equations 4. Multiply the first equation by -2 1.

Solve using elimination. 2 x – 3 y = -2 x + 3 y = 17 1. 2. 3. 4. (2, 2) (9, 3) (4, 5) (5, 4)

Board Drill Solve the system. x + y = 6 4 x – y = 19

Answer ( 5 , 1 )

Board Drill Solve the system 8 x + 5 y = 38 -8 x + 2 y = 4

Answer ( 1 , 6 )

Board Drill 3 x + 4 y = -6 -3 x + 2 y = 6

Answer ( - 2 , 0 )

Board Drill x – y = 11 2 x + y = 19

Answer ( 10 , -1 )

Board Drill 4 x + 3 y = 2 5 x + 3 y = -2

Answer ( - 4 , 6 )

Board Drill 5 x – 2 y = 24 3 x + 2 y = 24

Answer ( 6 , 3 )