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ALGEBRA II HONORS/GIFTED @

Learn to solve linear systems of equations through graphing, substitution, and elimination methods. Practice problems and step-by-step solutions provided. Identify independent, dependent, or inconsistent systems without graphing. Explore different scenarios and solutions.

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ALGEBRA II HONORS/GIFTED @

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  1. ALGEBRA II HONORS/GIFTED @ SECTIONS 3-1 and 3-2 : SOLVE LINEAR SYSTEMS OF EQUATIONS

  2. 1) Solve by graphing. 2x + y = 8 3x – 2y = -2 Solve for y. y = -2x + 8 Find the intercepts. x-int : -2/3 y-int : 1 The point of intersection is (2, 4) Note that 2(2) + 4 = 8 and 3(2) – 2(4) = -2

  3. 2) Solve by substitution. 3x – 2(-2x + 8) = -2 3x + 4x – 16 = -2 7x – 16 = -2 7x = 14 x = 2 2x + y = 8 3x – 2y = -2 Look for the equation where solving for x or for y is easiest. Substitute 2 for x for find y. y = -2(2) + 8 = 4 Solve for y in the top equation. y = -2x + 8 Next, substitute into the other equation and solve. 3x – 2y = -2 Therefore, the answer is (2, 4)

  4. 3) Solve using elimination 2 • (2x + y) = 8 • 2 3x – 2y = -2 4x + 2y = 16 3x – 2y = -2 2x + y = 8 3x – 2y = -2 7x = 14 x = 2 The goal is to make opposites for one of the variables and add the equations together. Substitute 2 for x into either original equation to find y. 2(2) + y = 8 4 + y = 8 y = 4 Multiply the top equation by 2 to make 2y on top to go along with the -2y on bottom. Therefore, the answer is (2, 4)

  5. METHODS FOR SOLVING SYSTEMS OF EQUATIONS : • Graphing • Substitution • Elimination (linear combination) • ???? • ????

  6. Solve using the method of your choice. 4) 3x – 7y = 31 2x + 5y = 11 5) 4x + 3y = 10 5x - y = 22 ANSWER : (4, -2) ANSWER : (8, -1)

  7. 6) 2x – 3y = 12 y = -2x + 4 Just in case you want it!! ANSWER : (3, -2)

  8. 7) y = x + 1 y = x – 2 8) 2x – 4y = -16 -x + 2y = 8 If the variables cancel false statement no solutions parallel lines true statement infinite solutions same lines

  9. 9) 4x – 3y = 11 5x – 6y = 9 10) (2, -3) 11) Silver Alloy Problem. Old silver coins contain 90% silver. Silver solder contains 63% silver. If you wanted to make 200 kg. of an alloy containing 82% silver, how many kg. of old coins and how many kg. of silver solder could you melt together to do this? 140.74 kg. coins and 59.26 kg. silver solder

  10. NAMES FOR SYSTEMS OF EQUATIONS Inconsistent equations Parallel lines Dependent equations Coincidental lines Independent equations Intersecting lines

  11. Without graphing, classify each system as independent, dependent, or inconsistent. 11) 4x – 5y = 0 3x – 5y = -5 12) -20x + 12y = -24 5x - 3y = 6 ANSWER : dependent ANSWER : independent 13) 3x - y = 2 6x – 2y = 5 ANSWER : inconsistent

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