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1. 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
2. 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.
3. 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.
4. 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
5. 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
6. Slide 6 - Solve using elimination.

• 2x – 3y = -2
• x + 3y = 17
• (2, 2)
• (9, 3)
• (4, 5)
• (5, 4)
7. 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.
8. 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

• 14 and 4
• 20 and -2
• 24 and -6
• 30 and 8