Solving Systems of Linear Equations in 3 Variables.

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Solving Systems of Linear Equations in 3 Variables. Section 4.2 Solving Systems of Linear Equations in 3 Variables.

Small differences… This time, the solution is an ordered triple: (x, y, z). EX: Is (2, -2, 1) a solution to: 3x + 2y + z = 3 2x – 3y – 2z = 8 -2x+ 4y + 3z = -9

To Solve (Elimination Method) Select 2 equations and multiply to get one variable to have opposite coefficients. Add to eliminate that variable. Select 2 DIFFERENT equations and eliminate the same variable. Solve for the 2 remaining variables using methods from section 4.1. Substitute the values just found into any of the original equations and solve for the 3rd variable.

Solve each 1) x + y + z = 2 2) 2x + 3y - 2z = -4 3x + y - z = -2 4x – 3y + z = 25 2x – 2y + 3z = 15 x + 2y – 4z = -12 3) z = -3x + y – 10 4) -8x + 4y + 6z = -18 2x + 3y – 2z = 5 2x – y – 1.5z = 4.5 x = 3y – 3z – 14 4x – 2y – 3z = 9