SolveSysByElimAddSub

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Slide 1  Objective
 The student will be able to:
 solve systems of equations using elimination with addition and subtraction.
 SOL: A.4e
 Designed by Skip Tyler, Varina High School

Slide 2  Solving Systems of Equations
 So far, we have solved systems using graphing and substitution. These notes show how to solve the system algebraically using ELIMINATION with addition and subtraction.
 Elimination is easiest when the equations are in standard form.

Slide 3
 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.
 Step 3: Add the equations.
 Step 4: Plug back in to find the other variable.
 Step 5: Check your solution.
 Standard Form: Ax + By = C
 Look for variables that have the
 same coefficient.
 Solve for the variable.
 Substitute the value of the variable
 into the equation.
 Substitute your ordered pair into
 BOTH equations.

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

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

Slide 6  Solve using elimination.
 2x – 3y = 2
 x + 3y = 17
 (2, 2)
 (9, 3)
 (4, 5)
 (5, 4)

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

Slide 8  2) Solve the system using elimination.
 Step 4: Plug back in to find the other variable.
 y = 7 – 2x
 y = 7 – 2(2)
 y = 3
 Step 5: Check your solution.
 (2, 3)
 (3) = 7 – 2(2)
 4(2)  (3) = 5
 y = 7 – 2x
 4x  y = 5

Slide 10  Find two numbers whose sum is 18 and whose difference 22.

Slide 11  Find two numbers whose sum is 18 and whose difference 22.
 14 and 4
 20 and 2
 24 and 6
 30 and 8