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Algebra II Honors: Systems with 3 Variables

Learn how to solve systems of equations with three variables in Algebra II Honors class. Explore examples and find solutions using substitution and elimination methods.

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Algebra II Honors: Systems with 3 Variables

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  1. ALGEBRA II HONORS/GIFTED @ SECTION 3-5 : SYSTEMS 3 VARIABLES

  2. 1) Solve. 3x + 2y – 4z = 1 5x – 3y + 7z = 28 2x – 4y + 3z = 17 Step 2 – Use equations 1 & 3 to eliminate the same variable. 2 • 3 • 2 • 6x + 4y – 8z = 2 2x – 4y + 3z = 17 Step 1 – Choose a variable to eliminate, then use equations 1 and 2 to eliminate that variable. 8x - 5z = 19 Eliminate y. Number the equations 1-3 in order. 9x + 6y – 12z = 3 10x – 6y + 14z = 56 19x + 2z = 59

  3. Step 3 – Use the answers from steps 1 and 2 to find two of the variables. Step 4 – Substitute the answers from step 3 into an original equation to find the third variable. 5 • 19x + 2z = 59 3(3) + 2y – 4(1) = 1 9 + 2y – 4 = 1 5 + 2y = 1 2y = -4 y = -2 2 • 8x - 5z = 19 95x + 10z = 295 16x – 10z = 38 111x = 333 x = 3 8(3) – 5z = 19 24 - 5z = 19 -5z = -5 z = 1 Therefore, the answer is the ordered triple (3, -2, 1)

  4. 2) 2x - y - z = 7 3x + 5y + z = -10 4x – 3y + 2z = 4 ANSWER : (1, -2, -3)

  5. 3) Three robot prototypes, a Wat1000, a UB41, and a Pi314, agreed to race. The sum of their speeds was 30 miles per hour. The Pi314’s speed plus one-third of the Wat1000’s speed was 22 miles per hour more than the UB41’s speed. Four times the Wat1000’s speed plus three times the UB41’s speed minus twice the Pi314’s speed was 12 miles per hour. Find out how fast each robot ran. Then, tell what was unfortunate about the UB41. Answer : Wat1000 – 12 mph, Pi314 – 18 mph, UB41 – 0 mph, can’t run)

  6. 4) 5x + 2y - z = -8 x – 7y + 4z = 6 10x + 4y – 2z = -16 ANSWER : infinitely many solutions

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