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Solve the system: 2 x 14 3x 4 y 9 4 x 6 y 3 z 13 (7,3,1) Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Solving Systems of Equations Solve the system: 2 x 4 z 8 3 x 2 z 12 x y z 1 (2,-6,3) Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Solving Systems of Equations Solve the system: 2 x y 3z 1 x yz 0 3x 3 y 2 z 1 Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. What about this one? Step 1: Reduce the system to two equations in two variables using elimination. Step 2: Solve the resulting system of two equations using elimination or substitution. Step 3: Substitute the solutions in Step 2 into any of the original equations and solve for the third variable. Step 4: Check the solution in each of the three original equations. Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Solving Systems of Linear Equations with Three Variables Using Elimination and Substitution Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. What do equations with three variables look like? Solve the system: 2 x y 3 z 1 x yz 0 3x 3 y 2 z 1 Click mouse to continue Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn! Equation 1 : 2x y 3z 1 Equation 2 : x y z 0 Equation 3 : 3 x 3y 2z 1 Eliminate y Add equation 1 equation 2 2 x y 3z 1 xy z 0 3 x 2z 1 Add 3 times equation 1 equation 3 6 x 3y 9z 3 3 x 3y 2z 1 9 x 7z 2 Click mouse to continue with answer Answer 1 of 3 Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn! Eliminate x from the two variable system. 3 x 2z 1 9 x 7z 2 9 x 6z 3 9 x 7z 2 z 1 Substitute back to solve for x. 3x 21 1 3 x 3 x 1 Substitue back to solve for y. 1 y 1 0 y 2 Click mouse to continue with answer Answer 2 of 3 Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn! Check that x 1, y 2, z 1 satisfy all three equations 2 1 2 3 1 1 1 2 1 0 3 1 3 2 2 1 1 ( 1, 2,1) Answer 3 of 3 Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn! P900-903: 3, 5, 13, 15, 31, 33, 41, 47-49 Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. HOMEWORK