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3.2.1 – Linear Systems, Substitution

3.2.1 – Linear Systems, Substitution. A system of linear equations is two or more equations, with two or more variables, that we need to solve for We’ll generally stick with only two variables, x and y. Methods.

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3.2.1 – Linear Systems, Substitution

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  1. 3.2.1 – Linear Systems, Substitution

  2. A system of linear equations is two or more equations, with two or more variables, that we need to solve for • We’ll generally stick with only two variables, x and y

  3. Methods • There are various methods to use; some are more difficult than others, but we will have many options to use pending what case we have

  4. Solutions • The solutions to the system of equations we deal with are the ordered pair (x, y) • The x and y we find MUST work for both equations

  5. Example. • 3x – y = 3 • x + 2y = 8 • The above is example of a system. What is different than the equations we have solved before?

  6. Substitution • The first method we will use is substitution • 1) Pick an equation, and solve for one variable (try to pick the one which is easiest to solve for) • 2) Substitute the expression you find into the other equation • 3) Combine any like terms, distribute, etc., and solve for the remaining variable • 4) Go back and find the other variable

  7. Example. Solve the following system. • y = 2x • 4x – y = 6 • Is one variable already solved for?

  8. Example. Solve the following system. • x – 2y = -3 • 3x + 2y = 7 • Which variable is easiest to solve for?

  9. Example. Solve the following system. • 2x + y = 3 • 3x + y = 0

  10. Now, try the following 3 problems with people around you. Write down your answers and we will check with other people. • 1) m = 6n 2m – 4n = 16 • 2) x = y + 2 5x – 2y = 7 • 3) x = -y + 5 2x – y = 1

  11. Assignment • Pg. 125 • 3-6, 17-27 odd, 36

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