# Solve Systems By Elimination (Multiply First)

Created 3 years ago

Duration 0:12:08
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Slide Content
1. ### Slide 1 - Objective

• The student will be able to:
• solve systems of equations using elimination with multiplication.
• SOL: A.4e
• Designed by Skip Tyler, Varina High School
2. ### Slide 2 - Solving Systems of Equations

• These notes go one step further and show how to use ELIMINATION with multiplication.
• What happens when the coefficients are not the same?
• We multiply the equations to make them the same! You’ll see…
3. ### Slide 3

• Solving a system of equations by elimination using multiplication.
• Step 1: Put the equations in Standard Form.
• Step 2: Determine which variable to eliminate.
• Step 3: Multiply the equations and solve.
• 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.

• 2x + 2y = 6
• 3x – y = 5
• Step 1: Put the equations in Standard Form.
• Step 2: Determine which variable to eliminate.
• None of the coefficients are the same!
• Find the least common multiple of each variable.
• LCM = 6x, LCM = 2y
• Which is easier to obtain?
• 2y(you only have to multiplythe bottom equation by 2)
5. ### Slide 5 - 1) Solve the system using elimination.

• Step 4: Plug back in to find the other variable.
• 2(2) + 2y = 6
• 4 + 2y = 6
• 2y = 2
• y = 1
• 2x + 2y = 6
• 3x – y = 5
• Step 3: Multiply the equations and solve.
• Multiply the bottom equation by 2
• 2x + 2y = 6
• (2)(3x – y = 5)
• 8x = 16
• x = 2
• 2x + 2y = 6
• (+) 6x – 2y = 10
6. ### Slide 6 - 1) Solve the system using elimination.

• Step 5: Check your solution.
• (2, 1)
• 2(2) + 2(1) = 6
• 3(2) - (1) = 5
• 2x + 2y = 6
• 3x – y = 5
• Solving with multiplication adds one more step to the elimination process.
7. ### Slide 7 - 2) Solve the system using elimination.

• x + 4y = 7
• 4x – 3y = 9
• Step 1: Put the equations in Standard Form.
• Step 2: Determine which variable to eliminate.
• Find the least common multiple of each variable.
• LCM = 4x, LCM = 12y
• Which is easier to obtain?
• 4x(you only have to multiplythe top equation by -4 to make them inverses)
8. ### Slide 8 - 2) Solve the system using elimination.

• x + 4y = 7
• 4x – 3y = 9
• Step 4: Plug back in to find the other variable.
• x + 4(1) = 7
• x + 4 = 7
• x = 3
• Step 3: Multiply the equations and solve.
• Multiply the top equation by -4
• (-4)(x + 4y = 7)
• 4x – 3y = 9)
• y = 1
• -4x – 16y = -28
• (+) 4x – 3y = 9
• -19y = -19
9. ### Slide 9 - 2) Solve the system using elimination.

• Step 5: Check your solution.
• (3, 1)
• (3) + 4(1) = 7
• 4(3) - 3(1) = 9
• x + 4y = 7
• 4x – 3y = 9
10. ### Slide 10 - What is the first step when solving with elimination?

• Add or subtract the equations.
• Multiply the equations.
• Plug numbers into the equation.
• Solve for a variable.
• Determine which variable to eliminate.
• Put the equations in standard form.
11. ### Slide 11 - Which variable is easier to eliminate?

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• 3x + y = 4
• 4x + 4y = 6
• x
• y
• 6
• 4
12. ### Slide 12 - 3) Solve the system using elimination.

• 3x + 4y = -1
• 4x – 3y = 7
• Step 1: Put the equations in Standard Form.
• Step 2: Determine which variable to eliminate.
• Find the least common multiple of each variable.
• LCM = 12x, LCM = 12y
• Which is easier to obtain?
• Either! I’ll pick y because the signs are already opposite.
13. ### Slide 13 - 3) Solve the system using elimination.

• 3x + 4y = -1
• 4x – 3y = 7
• Step 4: Plug back in to find the other variable.
• 3(1) + 4y = -1
• 3 + 4y = -1
• 4y = -4
• y = -1
• Step 3: Multiply the equations and solve.
• Multiply both equations
• (3)(3x + 4y = -1)
• (4)(4x – 3y = 7)
• x = 1
• 9x + 12y = -3
• (+) 16x – 12y = 28
• 25x = 25
14. ### Slide 14 - 3) Solve the system using elimination.

• Step 5: Check your solution.
• (1, -1)
• 3(1) + 4(-1) = -1
• 4(1) - 3(-1) = 7
• 3x + 4y = -1
• 4x – 3y = 7
15. ### Slide 15 - What is the best number to multiply the top equation by to eliminate the x’s?

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• 3x + y = 4
• 6x + 4y = 6
• -4
• -2
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• 4
16. ### Slide 16 - Solve using elimination.

• 2x – 3y = 1
• x + 2y = -3
• (2, 1)
• (1, -2)
• (5, 3)
• (-1, -1)