9.2 Systems of Equations in Three Variables

  • Solve systems of linear equations in three variables.

  • Use systems of three equations to solve applied problems.

  • Model a situation using a quadratic function.

A linear equation in three variables is an equation equivalent to one of the form Ax+By+Cz=D, where A, B, C, and D are real numbers and none of A, B, and C is 0. A solution of a system of three equations in three variables is an ordered triple that makes all three equations true. For example, the triple (2, -1, 0) is a solution of the system of equations

4x+2y+5z=6,2xy+z=5,3x+2yz=4.

We can verify this by substituting 2 for x, 1 for y, and 0 for z in each equation.

Solving Systems of Equations in Three Variables

We will solve systems ...

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