Solving Systems of Equations by Elimination
Learn how to solve systems of equations by elimination method through examples, warm-up exercises, steps for elimination, and practice problems. Master this technique to find the unique values that make the equations true. Get ready to enhance your algebra skills with step-by-step guidance and visual aids.
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EQ: How do we solve Systems of Equations by Elimination?
Warm Up/Activating Strategy 1. Find the numbers that make the equations true for the following. ____ + __-5__ = 0 __2_ + ____ = 0 (___)_5_ + _-10_ = 0 2. In your own words what do you see that is unique about the numbers that equal to zero? What are these numbers called?
Steps for Elimination: 1. Arrange the equations with like terms in columns 2. Multiply, if necessary, to create opposite coefficients for one variable. 3. Add the equations. 4. Substitute the value to solve for the other variable. 5. Check
EXAMPLE 1 (continued) 2 2 x x 2 2 y y 8 + = = 4 (-1, 3)
EXAMPLE 2 4x + 3y = 16 2x 3y = 8 (4, 0)
EXAMPLE 3 3x + 2y = 7 -3x + 4y = 5 (1, 2)
EXAMPLE 4 2x 3y = 4 -4x + 5y = -8 (2, 0)
EXAMPLE 5 2x + 3y = 1 4x 2y = 10 (2, -1)
EXAMPLE 6 5x + 2y = 7 -4x + y = 16 (3, -4)
Classwork Please solve the first set of practice problems #1-9. I have provided an answer key. Here is a link for instructions if you need help working them out. The second set of problems you will work on your own. I will provide key so you can check as you go. Please free to ask questions. You will be assigned 5 questions at the end of the lesson to turn in.
Practice Problems Set 1 Use elimination to solve each system of equations. 1. 6x + 5y = 4 2. 3m 4n = -14 3. 3a + b = 1 6x 7y = -20 3m + 2n = -2 a + b = 3 1, 4) 2, 2) 1, 2) 4. -3x 4y = -23 5. x 3y = 11 6. x 2y = 6 -3x + y = 2 2x 3y = 16 x + y = 3 (1, 5) 7. 2a 3b = -13 8. 4x + 2y = 6 2a + 2b = 7 4x + 4y = 10 (5, 2) (4, 1) 9. 5x y = 6 5x + 2y = 3 1/2, 4) (1/2, 2) (1, 1)
Set 2 Practice Problems Use elimination to solve each system of equations. 1. 2x + 3y = 6 2. 2m + 3n = 4 3. 3a - b = 2 x + 2y = 5 -m + 2n = 5 a + 2b = 3 (1, 1) 1, 2) 3, 4) 4. 4x + 5y = 6 5. 4x 3y = 22 6. 3x 4y = -4 6x - 7y = -20 2x y = 10 x + 3y = -10 1, 2) (4, 2) 4, 2) 7. 4x y = 9 5x + 2y = 8 2a + 2b = 3 8. 4a 3b = -8 9. 2x + 2y = 5 4x - 4y = 10 (2, 1) 1/2, 2) (2.5, 0)
Homework Practice Worksheet
